Introduction
============

Salivary adenoid cystic carcinoma (SACC), which is a common malignant tumor of the oral and maxillofacial region, originates from myoepithelial and basal cells, and although this tumor type grows slowly, it has a high capacity for invasion ([@b1-etm-0-0-4902],[@b2-etm-0-0-4902]). SACC easily disseminates to distant organs through the bloodstream, and the most common organ of distant metastases is the lung ([@b3-etm-0-0-4902]). Clinically, as the main cause of death in patients with SACC, lung metastasis initially occurs as a distant metastasis of SACC and is frequently observed before the first diagnosis. Studies have shown that cumulative lung metastasis rates at 5 and 10 years can be as high as 70 and 100%, respectively. The high lung metastatic characteristics of SACC significantly reduce the long-term survival rate. Studies have reported that the overall survival rate (60 months) of patients with SACC is 71%, whereas the overall survival rate (180 months) is only 37%. However, the 5- and 15-year survival rates of patients diagnosed with lung metastasis are only 35 and 0%, respectively ([@b4-etm-0-0-4902]). Currently, chemotherapy is the major strategy used to treat lung metastasis. However, traditional chemotherapy drugs have poor solubility and poor targeting, and their use may therefore lead to many side effects and the potential development of drug resistance, which has a significant impact on the effectiveness of chemotherapy.

Recently, new types of hyperbranched polymers have been developed for use as drug delivery systems ([@b5-etm-0-0-4902]). The use of hyperbranched polymers in the field of biomedicine has only recently emerged ([@b6-etm-0-0-4902]). As a new drug delivery system, hyperbranched polymers have many excellent properties, including ligand targeting and a large number of terminal functional groups, which can be used to connect drug molecules and fluorescence groups. Different molecular structures can provide a variety of drug delivery pathways. Sensitive responsiveness to environmental stimuli can be used to build an intelligent drug-controlled release system; the relatively small hydrodynamic radius is conducive to the improvement of the efficiency of cell uptake ([@b7-etm-0-0-4902]). The emergence of hyperbranched polymer drug delivery systems provides a good choice for the improvement of the efficacy of chemotherapy for adenoid cystic carcinoma.

Therefore, we used glycerol and glycidyl methacrylate as raw materials to synthesize dHPG. The characterization of dHPG was detected using the nuclear magnetic resonance (NMR) and Fourier transform infrared spectroscopy (FTIR) techniques. An antineoplastic drug, specifically hydroxycamptothecin (HPT), was conjugated onto the surface of dHPG. The drug loading efficiency (DLE) of the resultant HPT-conjugated polymers (dHPG-HPT) was 5.66 wt% ([@b8-etm-0-0-4902]). dHPG-HPT was used as a treatment, and the growth of the SACC xenografts in nude mice was observed. Thus, the aim of the present study was to provide new solutions and theoretical bases for clinical chemotherapy.

Materials and methods
=====================

### Cell culture

SACC cells with a high potential for pulmonary metastasis (SACC-LM cells) were a gift from the Department of Oral and Maxillofacial Surgery, School of Stomatology, Peking University (Beijing, China). The cells were cultured in DMEM supplemented with 10% fetal bovine serum and 2% penicillin/streptomycin at 37°C with 5% CO~2~.

### Xenograft study

Sixteen four-week-old female BALB⁄c nu⁄nu nude mice were inoculated with 4×10^6^ SACC-LM cells in 200 µl of culture medium via the tail vein. Four weeks after inoculation, 4 of the animals were euthanized, and their lungs were removed. Metastatic nodules were observed on the surface of the lungs, which indicated the successful establishment of the animal model of SACC lung metastasis. Subsequently, the remaining animals were randomly divided into the following three groups: Control, HPT and dHPG-HPT group. With regard to treatment, 0.2 ml of 0.9% saline was injected into the tail vein of nude mice in the control group; 0.2 mg of HPT (Biochempartner Co, Ltd, Shanghai, China) at a concentration of 1 µg/ml was injected into the tail vein of nude mice in the HPT group; and dHPG-HPT (synthesized as described in our previous study) containing the same concentration of HPT was injected into the tail vein of nude mice in the dHPG-HPT group. The treatment was implemented twice a week for two weeks. After two weeks, all mice were euthanized, and their lungs were removed. Finally, the lungs were paraffin-embedded for H&E and immunohistochemical staining analyses. The study protocol was approved by the local Animal Ethics Committee of Tongji University (Shanghai, China) (project no. 2016--009) and was conducted in accordance with the local and state regulations regarding the use of animals for experimental purposes.

### H&E staining

The lungs were immersed in 4% paraformaldehyde for 4 h and transferred to 70% ethanol. The individual lobes of the lung were placed in processing cassettes, dehydrated through a serial alcohol gradient, and embedded in paraffin wax blocks. Prior to staining, 4-µm-thick lung tissue sections were deparaffinized in xylene, rehydrated through decreasing concentrations of ethanol, and washed in phosphate-buffered saline (PBS). Subsequently, the tissue sections were stained with H&E. After staining, the sections were dehydrated through increasing concentrations of ethanol and xylene.

### Immunohistochemical staining

Immunohistochemical studies of the lung tissue were conducted using the following antibodies: Monoclonal rabbit anti-mouse vascular endothelial growth factor (VEGF; ab1316), cluster of differentiation (CD34; ab81289), proliferating cell nuclear antigen (PCNA; ab92552), and MMP9 (ab58803) (dilution 1:400), which were all purchased from Abcam (Cambridge, UK); biotinylated goat anti-rabbit IgG was used as the secondary antibody. An S-P kit (Gene Tech Biotechnology Co., Ltd., Shanghai, China) was used for the immunohistochemistry experiments. Briefly, the paraffin sections were deparaffinized in xylene and rehydrated in an alcohol gradient. Antigen retrieval was performed by microwave treatment in 0.01 M sodium citrate buffer (pH=6.0) for 15 min, after which the slides were cooled to room temperature for 1 h, and subsequently washed with PBS. Endogenous peroxidase activity was inactivated with 0.3% hydrogen peroxide for 30 min and non-specific protein interactions were blocked with an avidin/biotin blocking solution containing 10% normal goat serum. The sections were subsequently incubated overnight with primary antibodies against VEGF, CD34, PCNA, and MMP9. The immunoreactions were detected after staining with 3,3′-diaminobenzidine.

### Scoring of the immunohistochemistry results

The signal intensities of VEGF and MMP9 were measured using Image-Pro Plus. Briefly, five fields of view were randomly selected, and the integrated optical density (IOD) (sum) and area (sum) of the fields were calculated. The mean optical density was calculated as the IOD (sum)/area (sum).

The nuclei of PCNA-positive cells were stained brown. Five fields of PCNA staining were observed at high magnification under light microscopy, and the number of positive cells was counted. The positive CD34 signal was calculated using Weidner\'s method ([@b9-etm-0-0-4902]). The criteria for positive staining included the following:

1.  A vascular endothelial cell or endothelial cell cluster, isolated from the peripheral vasculature, tumor cell or other connective tissue identified as a single microvessel.

2.  A vessel derived from the same microvascular endothelial cells, which are clear and separated from each other, and can be counted as a separate microvessel.

3.  Red blood cells are not necessary to confirm microvessels.

4.  Vessels in the sparse region of tumor cells and adjacent benign tissue regions were not counted.

5.  Vessels with a luminal diameter of \>10 erythrocytes were not counted.

The entire section was observed to determine the high blood vessel density and the 'Hot spot' at low magnification, ×40. Subsequently, the number of blood vessels stained brown was counted at high magnification, ×200. Two people conducted this procedure using a double-blind method.

### Statistical analysis

The statistical analyses were performed using SPSS 20.0. All quantitative data were expressed as the means ± SEM for each condition. The data were tested for statistical significance using one-way analysis of variance (ANOVA). P\<0.05 (F values \>Fα) were considered to indicate a statistically significant difference.

Results
=======

### dHPG-HPT inhibits xenograft growth

We initially dissected the lungs of the nude mice in each group and observed that the volumes of the lungs in the control group were the highest ([Fig. 1A](#f1-etm-0-0-4902){ref-type="fig"}), the metastatic nodules were large, and the lungs were deformed. Several metastatic nodules were observed on the surface of the lungs of mice in the HPT group ([Fig. 1B](#f1-etm-0-0-4902){ref-type="fig"}). The lungs of mice in the dHPG-HPT group were most similar to those of mice in the control group, as few metastatic nodules were observed on the lungs ([Fig. 1C](#f1-etm-0-0-4902){ref-type="fig"}).

Next, we observed the histological aspect of the lungs by H&E staining ([Fig. 2](#f2-etm-0-0-4902){ref-type="fig"}). In the control group, a major portion of the lungs was occupied by solid tumor tissue ([Fig. 2A](#f2-etm-0-0-4902){ref-type="fig"}). At high magnification, the solid tumor tissue was filled with SACC cells ([Fig. 2D](#f2-etm-0-0-4902){ref-type="fig"}). In the HPT group, approximately half of the tissue consisted of solid tumor ([Fig. 2B](#f2-etm-0-0-4902){ref-type="fig"}). In contrast to the HPT group, only a few metastatic nodules were observed in the lungs of mice in the dHPG-HPT group ([Fig. 2C](#f2-etm-0-0-4902){ref-type="fig"}); a major portion of the tissue was reticular lung tissue.

### dHPG-HPT reduces the expression of VEGF and CD34

Angiogenesis plays an important role in the growth of tumors. To explore the molecular differences in angiogenesis in each group, we used immunohistochemistry to detect the expression of VEGF and CD34. Immunohistochemical staining ([Fig. 3](#f3-etm-0-0-4902){ref-type="fig"}) of the tumor xenograft showed a marked reduction in the expression of VEGF in the dHPG-HPT group compared with the HPT group \[IOD (sum)/area (sum)\]: dHPG-HPT, 0.02 vs. HPT, 0.04; P\<0.01) ([Fig. 3D](#f3-etm-0-0-4902){ref-type="fig"}).

Furthermore, microvessel density (MVD; [Fig. 4](#f4-etm-0-0-4902){ref-type="fig"}), which was based on CD34 expression, was significantly lower in the dHPG-HPT group compared with the HPT group ([Fig. 4D](#f4-etm-0-0-4902){ref-type="fig"}). This result indicated that dHPG-HPT could reduce angiogenesis in SACC.

### dHPG-HPT inhibits the proliferation of SACC cells

We next investigated the inhibitory effect of dHPG-HPT on the proliferation of SACC cells. Immunohistochemistry ([Fig. 5](#f5-etm-0-0-4902){ref-type="fig"}) showed that the number of PCNA-positive cells in tumors of the dHPG-HPT group was significantly lower than that in tumors of the HPT and control groups (dHPG-HPT: 5±1.15; HPT: 29±1.74; control: 60±2.53) ([Fig. 5D](#f5-etm-0-0-4902){ref-type="fig"}). This result suggested that dHPG-HPT may be more efficient in the inhibition of SACC cell proliferation.

### dHPG-HPT may inhibit the invasion capacity of SACC cells

Matrix metalloproteinase 9 (MMP9) plays a critical role in tumor invasion and metastasis ([@b10-etm-0-0-4902]). Immunohistochemistry ([Fig. 6](#f6-etm-0-0-4902){ref-type="fig"}) showed that the expression of MMP9 in tumors of the dHPG-HPT group was dramatically decreased compared with that in tumors of the HPT group (IOD (sum)/area (sum): dHPG-HPT, 0.005 vs. HPT, 0.03; P\<0.01) ([Fig. 6D](#f6-etm-0-0-4902){ref-type="fig"}). This result suggested that dHPG-HPT may be more efficient in the inhibition of the invasion and metastasis of SACC cells.

Discussion
==========

As a drug carrier, dHPG has many advantages. First, this compound has a large number of terminal functional groups, which can be used to conjugate drugs and fluorescent groups. Second, dHPG has good solubility and dissolves in the blood, which carries the drugs to tissues, which indicates limited drug toxicity and side effects. Moreover, as a drug carrier, dHPG can be degraded *in vivo*, and the resulting non-toxic degradation products can be absorbed and metabolized. Furthermore, dHPG can target tumor tissues through the 'enhanced permeability and retention' (EPR) effect and release the drugs only in the targeted tissues. Thus, gross observation revealed that the number of SACC metastatic nodules in the lungs was significantly decreased in the dHPG-HPT group compared with the HPT group, suggesting that compared with HPT, dHPG-HPT was more capable of inhibiting the growth of SACC lung metastasis *in vivo*.

The passive accumulation of macromolecules (\>20 kDa) in solid tumors is a phenomenon that might be a potential biological target for tumor-selective drug delivery. The rationale for the use of macromolecules as efficient carriers for the delivery of antitumor agents, even if these molecules are not targeted to an antigen or receptor on the surface of the tumor cell, is based on the work of Matsumura and Maeda ([@b11-etm-0-0-4902]). Differences in the biochemical and physiological characteristics of normal and malignant tissues are responsible for the passive accumulation of macromolecules in tumors. This feature, termed the EPR effect ([@b12-etm-0-0-4902],[@b13-etm-0-0-4902]), is schematically depicted in [Fig. 7](#f7-etm-0-0-4902){ref-type="fig"}. Briefly, low-molecular-weight compounds can easily diffuse into normal and tumor tissues through the endothelial cell layer of blood capillaries. However, macromolecules cannot pass through the capillary walls of normal tissues. Macromolecules enter tumor tissues through the capillaries where blood flow is diminished. In contrast to most normal tissues, tumor tissues are rich in new capillaries, and the endothelial layer of the capillaries is fenestrated and leaky; thus, macromolecules and other nanoparticles can reach the malignant tissue. Tumor tissue generally has a defective lymphatic drainage system, resulting in the retention and subsequent accumulation of macromolecules in solid tumors. Due to the EPR effect, compared with HPT, dHPG-HPT can passively accumulate in SACC xenografts and is sustained for a long period of time, which significantly reduces the volume of lung metastases in nude mice and confers a better treatment effect.

VEGF also plays an important role in angiogenesis ([@b14-etm-0-0-4902]--[@b16-etm-0-0-4902]) through the promotion of chemotaxis and mitosis of vascular endothelial cells via the targeting of the specific receptors VEGFR-1 and VEGFR-2, which promotes the growth of tumor tissues. In addition, VEGF enhances the vascular permeability of normal blood vessels and tumor vessels ([@b17-etm-0-0-4902],[@b18-etm-0-0-4902]). Thus, VEGF is one of the critical factors that has an impact on the EPR effect. In the present study, the expression of VEGF in the control group was high, indicating that SACC xenografts were in a rapid growth phase; this potentially provides a good condition for the EPR effect. In the dHPG-HPT group, the expression of VEGF was low, and the tumor volumes were smaller than in the HPT group ([Fig. 3](#f3-etm-0-0-4902){ref-type="fig"}), which suggests that the growth of SACC xenografts was inhibited in the dHPG-HPT group. Due to the EPR effect, dHPG-HPT has a passive targeting effect on tumor tissue and a better inhibitory effect on the growth of tumor tissue; thus, the expression of VEGF in the dHPG-HPT group was reduced.

In 1992, Weidner *et al* ([@b9-etm-0-0-4902]) reported on MVD, which was used to quantify the amount of new blood vessels in tumors. CD34 is typically overexpressed in proliferating vascular endothelial cells and vascular endothelial cells in tumorous vascular tissues and is typically weakly expressed or absent in normal mature vascular endothelial cells. In [Fig. 4A](#f4-etm-0-0-4902){ref-type="fig"}, a large number of new CD34-positive microvessels was observed, and the MVD of the control group was high, suggesting that the tumor was rich in microvascular tissue. However, the MVD of the dHPG-HPT and HPT groups was less than that of the control group, suggesting that both HPT and dHPG-HPT exerted an inhibitory effect on pulmonary metastases of SACC. Since dHPG-HPT utilizes the EPR effect for a passive targeting effect, which can largely inhibit the formation of tumor tissue, the amount of neovascularization in tumor tissue and the MVD of tumor tissue is reduced, and therefore, the MVD was lowest in the dHPG-HPT group.

PCNA is an auxiliary component of DNA polymerase delta and is necessary for DNA replication. PCNA is synthesized during G1 phase of the cell cycle and its expression peaks during S phase, during which it plays an important role in the regulation of DNA replication. The synthesis and expression of PCNA is closely related to the cell proliferation status and is a major biological indicator that reflects the proliferation of cells ([@b19-etm-0-0-4902],[@b20-etm-0-0-4902]). In the control group, PCNA-positive cells were detected in the tumor tissue, and the number of positive cells was significantly higher than that in the other two groups ([Fig. 5](#f5-etm-0-0-4902){ref-type="fig"}), indicating that the SACC-derived tumors were in the proliferation phase. In contrast, the number of PCNA-positive cells was lower in the HPT group, as HPT exerted an inhibitory effect on the growth of SACC. The number of PCNA-positive cells was lowest in the dHPG-HPT group, indicating that dHPG-HPT showed the strongest inhibition of the proliferation of SACC.

A prerequisite for tumor invasion and metastasis is the destruction of the integrity of the basement membrane ([@b21-etm-0-0-4902]), which occurs during the interaction between tumor cells and the extracellular matrix. Matrix metalloproteinases (MMPs), which degrade extracellular matrix components, play a critical role in tissue remodeling during the development of pathological processes, including inflammation, tissue repair, tumor invasion, and metastasis ([@b10-etm-0-0-4902],[@b22-etm-0-0-4902]). Among MMPs, MMP9 is of particular interest because this protein, secreted in the form of a zymogen, is activated to form collagen IV and V as well as gelatin structures, such as the basement membrane and connective tissue. MMP9 plays an important role in tumor metastasis ([@b23-etm-0-0-4902],[@b24-etm-0-0-4902]). SACC has a strong capacity for invasion, easily invades local normal tissue and metastasizes to distal organs. Thus, the expression of MMP9 in the control group was highest ([Fig. 6](#f6-etm-0-0-4902){ref-type="fig"}). However, the expression of MMP9 in the HPT group was decreased and was lowest in the dHPG-HPT group, implying that both HPT and dHPG-HPT reduce the invasiveness and metastatic capability of SACC; between these two, dHPG-HPT led to a greater reduction.

dHPG-HPT can effectively reduce the expression of VEGF, CD34, PCNA and MMP9 in SACC xenografts and suppress angiogenesis, proliferation and invasion of SACC cells *in vivo*, indicating a good therapeutic effect on SACC xenografts in nude mice. This study provides a theoretical basis for the application of polymeric drug carriers in the treatment of SACC.

The present study was supported by the Shanghai Science and Technology Commission (no. 12nm0503002).

SACC

:   salivary adenoid cystic carcinoma

EPR

:   enhanced permeability and retention

![Gross images of metastatic lung tissue. (A) Control group; (B) HPT group; (C) dHPG-HPT group. The arrows indicate the metastatic nodules. Scale bar, 1 mm.](etm-14-04-3105-g00){#f1-etm-0-0-4902}

![(A-F) Histological aspects of the lungs (H&E). (A and D) Control group; (B and E) HPT group; (C and F) dHPG-HPT group. The arrows indicate the tumor tissues, and the triangles indicate normal lung tissue. Scale bar, 100 µm.](etm-14-04-3105-g01){#f2-etm-0-0-4902}

![The expression of VEGF in tissue samples from (A) the control group, (B) HPT group and (C) dHPG-HPT group. (D) Shows the IOD (sum)/area (sum) of each group. The arrows indicate the positive signal. Scale bar, 100 µm. \*P\<0.05.](etm-14-04-3105-g02){#f3-etm-0-0-4902}

![The expression of CD34 in the tissue samples of (A) the control group, (B) HPT group and (C) dHPG-HPT group. (D) Shows the number of microvessels in each group. The arrows indicate microvessels. Scale bar, 100 µm. \*P\<0.05.](etm-14-04-3105-g03){#f4-etm-0-0-4902}

![The expression of PCNA in the tissue samples of (A) the control group, (B) HPT group and (C) dHPG-HPT group. (D) Shows the number of positive cells in each group. The arrows indicate positive cells. Scale bars, 100 µm. \*P\<0.05.](etm-14-04-3105-g04){#f5-etm-0-0-4902}

![The expression of VEGF in the tissue samples of (A) the control group, (B) HPT group and (C) dHPG-HPT group. (D) Shows the IOD (sum)/area (sum) of each group. The arrows indicate the positive signal. Scale bar, 100 µm. \*P\<0.05.](etm-14-04-3105-g05){#f6-etm-0-0-4902}

![Schematic representation of the anatomical and physiological characteristics of normal and tumor tissue with respect to the EPR effect.](etm-14-04-3105-g06){#f7-etm-0-0-4902}


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Plus: Mexican papayas cause a small food-poisoning outbreak in Illinois; and American officials are pushing to broaden the types of E. coli that's subject to regulation, all in our morning news roundup.


Trans Latinas Seek City Funds

As transgender Latinas increasingly speak out about the discrimination and harassment they experience in San Francisco’s Mission district, a nonprofit is asking city officials to fund its work to prevent such violence.

El/La Para Translatinas emerged in 2006 after Proyecto ContraSIDA Por Vida, where it had been a program, lost its funding. It is mainly volunteer-led but has been able to tap into HIV funds in order to hire three part-time staffers.

"What we have at El/La is a lot of expertise and a lot of trust with trans Latinas. We created a space for trans Latinas and actually built community," said Marcia Ochoa, El/La’s unpaid program director.

Ochoa, who lives in Santa Cruz and teaches at the UC campus there, helped start El/La and travels to the city several times a week for the agency. Her academic work focuses on structural violence that trans women experience in Latin America and helped shape the agency’s approach.

"It is about the emergence of the trans movement and political consciousness now," said Ochoa, 42, who is gender variant and identifies as a butch lesbian.

As the discourse around the needs of the transgender community has matured, said Ochoa, there has been greater awareness that trans people are oftentimes excluded in efforts to fight poverty or violence.

"It used to be when people thought about these bread and butter issues that queer and trans people were not seen as ’part of’ but seen as ’additional’ to it," she said.

Or policies meant to help ended up working against trans people. Ochoa pointed to homeless shelters as one example where certain rules can prevent trans people from accessing such housing.

"We are moving into a new period where finally we are having some recognition of not only trans women in particular but transgender people in general," said Ochoa.

For years the city’s Department of Public Health has prioritized transgender women as being in need of HIV prevention services. As part of a collaborative of local agencies serving this population, El/La has received $90,000 a year that pays for an office coordinator, a health education coordinator, and an outreach coordinator who all work part-time.

El/La is now seeking an additional $80,000 from the city in order to hire a full-time case manager and expand the work it is doing around the domestic violence that trans Latinas experience.

"It would really supplement and complement what we are able to do," said Ochoa.

Violence against trans Latinas "is not a recent thing," pointed out Isa Noyola, 34, a transgender woman who has been with El/La for six years and serves as its volunteer office manager.

"Every year we are having to advocate for our community," she said. "We are dealing with the trauma that walks through our door when we are open for drop-in hours."

She added that El/La is "running at a very high level with very little. To me that is not sustainable."

In March El/La took part in a rally held to focus attention on several violent episodes involving trans women in the Mission. That led to the agency working with the office of gay District 9 Supervisor David Campos, who represents the Mission, on ways to bolster its funding.

Campos has become a vocal backer of El/La and helped raise $5,000 for the agency during a fundraiser last weekend that also netted enough money to save Mission gay bar Esta Noche.

He invited several El/La staffers and clients, including Noyola, to speak at a recent budget hearing Campos co-hosted with Mayor Ed Lee and gay District 8 Supervisor Scott Wiener. And he again pointed to the need for additional city resources for trans Latinas during a hearing he held last week at City Hall about the violence directed toward trans women.

"We need to set up a meeting with the key players to come up with a comprehensive strategy around the budget in terms of what additional resources are needed," Campos said during the May 16 hearing before the supervisors’ Neighborhood Services and Safety Committee, which he chairs. "We need to create domestic violence funding for the trans community."

El/La has also courted support this year from the San Francisco Domestic Violence Consortium, a collaborative between 17 agencies that advocates around the issue and lobbies for funding.

"We are certainly on their side and want them to be successful," said Beverly Upton, the consortium’s executive director.

The agency has begun conversations with the San Francisco Commission on the Status of Women about its funding process. While it has awarded grants to several nonprofits that serve transgender women, the commission has never directly funded an agency whose sole focus is on transgender clients.

Emily M. Murase, Ph.D., executive director of the city’s Commission on the Status of Women, attended and spoke at the board hearing. In a later interview with the Bay Area Reporter, she said that she recognizes there is an urgent need to address the issues brought up both in public and during a private meeting she had with El/La.

"Really, the extent of the harm of the violence against this particular demographic has become painfully clear to this department recently. So in the light of that, clearly there is unmet need here and we would like to do what we can," said Murase. "We are looking to see what options are available for how can we improve San Francisco’s response."

The commission operates on a three-year funding cycle. For fiscal years 2011-2012 through 2013-2014 it selected 25 different agencies, two of which are LGBT-focused, to share in $3.2 million earmarked for violence against women programs. It did not receive any requests for funding from a trans-specific program.

The commission is currently working on its next requests for funding, which would begin July 1, 2014. It is expected the lack of trans women programs will be highlighted in its next community needs assessment to be released sometime later this year.

It is possible that some funding for a trans program could be allocated off-cycle this year. If that were the case, El/La would have a chance to apply.

Ochoa expressed optimism about El/La receiving funding from the city for additional staff going forward.

"We are always cautiously optimistic," she said. "We could put them in place right away and make a huge difference in the lives of the people we work with day to day."

Until now the trans Latina program has not actively fought for additional funds, mainly due to being short staffed.

Noyola works full-time overseeing the workforce program for paid internships for LGBT youth at LYRIC, the Lavender Youth Recreation and Information Center. The agency serves as El/La’s fiscal sponsor and does receive funding from the Commission on the Status of Women for its Queer Young Women’s Health and Safety Project.

"For us, I think, we have kept insular for many reasons. We are definitely focused on the priorities of our women," Noyola told the B.A.R. "Our capacity to be part of so many different conversations in the city has been limited. To me, it is about kind of looking at reprioritizing where we are getting support."

Nor was El/La aware there is a vacant seat currently on the Commission on the Status of Women until asked about it by the B.A.R. The seat has been open since October.

The mayor appoints all seven commissioners who serve four-year terms. Currently, there is one lesbian member, political consultant Andrea Shorter.

There has not been a transgender appointee since March 2009, when Nikki Calma, also known by her drag name Tita Aida, resigned. Her appointment in 2008 marked the first time a trans woman had served on the commission.

It is unclear why Lee has yet to fill the seat, or if he is considering naming a trans woman. His spokespeople did not respond to the B.A.R. ’s request for comment, while staffers at the commission were unaware of a trans woman applying for the vacancy.

While Noyola and Ochoa both stated they believe it is important for a trans woman to serve on the commission, neither was sure they would have the time to do so themselves as they are already juggling their duties at their paid jobs with their volunteer work.

Part of their mission is to build the leadership skills of the women El/La serves so they can be public advocates. That can be difficult, though, when many of the trans women they see do not speak English.

"We are starting from the ground up. It has been challenging finding resources for our community that is linguistically appropriate," said Noyola. "The fact our women are coming out to speak publicly is due to our work. There needs to be representation, whether myself or someone else, who can speak for the trans Latina community, the immigrant community, and the monolingual community."

El/La is located at 2940 16th Street, Suite 319, at Capp. It is open Tuesday to Friday from 5 to 9 p.m.

Leave it to a six-time Tony Award winner Audra McDonald to add some major theatrics to the scene playing out over social media in response to Republican Indiana Gov. Mike Pence's signing of a "license to discriminate" bill Thursday.


LAN destination guide: Bolivia

Discover the charms of those places you always wanted to know with our destination guide. Here you will find the best information that only LAN Airlines and Lonely Planet, the largest travel publisher in the world, you can deliver.

Find out everything you need to know for your vacation in Bolivia and have an unforgettable time. "Content provided by LAN"

Bolivia

Bolivia is a country in central-western South America. Its capital is La Paz and it shares borders with Brazil, Argentina, Paraguay, Chile and Peru. Its geography is very varied, since you can see where the Altiplano joins the Andean foothills, as well as visiting the region of Chaco and the Amazon. Don’t put it off any longer, purchase your tickets to Bolivia and get to know the beauty of Santa Cruz de la Sierra, the snowcapped mountians of llimani, the archaeological remains of the Tiwanaku culture, Moon Valley and the famous Lake Titicaca, as well as many other tourist attractions. "Content provided by LAN"


1And when he had called unto him his twelve disciples, he gave them power against unclean spirits, to cast them out, and to heal all manner of sickness and all manner of disease.2Now the names of the twelve apostles are these; The first, Simon, who is called Peter, and Andrew his brother; James the son of Zebedee, and John his brother;3Philip, and Bartholomew; Thomas, and Matthew the tax collector; James the son of Alphaeus, and Lebbaeus, whose surname was Thaddaeus;4Simon the Canaanite, and Judas Iscariot, who also betrayed him.5These twelve Jesus sent forth, and commanded them, saying,
Go not into the way of the Gentiles, and into any city of the Samaritans enter you not:6But go rather to the lost sheep of the house of Israel.7And as you go, preach, saying, The kingdom of heaven is at hand.8Heal the sick, cleanse the lepers, raise the dead, cast out demons: freely you have received, freely give.9Provide neither gold, nor silver, nor brass in your purses,10Nor bag for your journey, neither two coats, neither shoes, nor yet a staff: for the workman is worthy of his food.11And into whatsoever city or town you shall enter, inquire who in it is worthy; and there abide till you go from there.12And when you come into a house, greet it.13And if the house be worthy, let your peace come upon it: but if it be not worthy, let your peace return to you.14And whoever shall not receive you, nor hear your words, when you depart out of that house or city, shake off the dust of your feet.15Verily I say unto you, It shall be more tolerable for the land of Sodom and Gomorrah in the day of judgment, than for that city.16Behold, I send you forth as sheep in the midst of wolves: be therefore wise as serpents, and harmless as doves.17But beware of men: for they will deliver you up to the councils, and they will scourge you in their synagogues;18And you shall be brought before governors and kings for my sake, for a testimony against them and the Gentiles.19But when they deliver you up, take no thought how or what you shall speak: for it shall be given you in that same hour what you shall speak.20For it is not you that speak, but the Spirit of your Father who speaks through you.21And the brother shall deliver up the brother to death, and the father the child: and the children shall rise up against their parents, and cause them to be put to death.22And you shall be hated of all men for my name's sake: but he that endures to the end shall be saved.23But when they persecute you in this city, flee into another: for verily I say unto you, You shall not have gone over the cities of Israel, till the Son of man comes.24The disciple is not above his teacher, nor the servant above his lord.25It is enough for the disciple that he be as his teacher, and the servant as his lord. If they have called the master of the house Beelzebub, how much more shall they call them of his household?26Fear them not therefore: for there is nothing covered, that shall not be revealed; and hid, that shall not be known.27What I tell you in darkness, that speak in light: and what you hear in the ear, that preach upon the housetops.28And fear not them who kill the body, but are not able to kill the soul: but rather fear him who is able to destroy both soul and body in hell.29Are not two sparrows sold for a farthing? and one of them shall not fall on the ground without your Father.30But the very hairs of your head are all numbered.31Fear not therefore, you are of more value than many sparrows.32Whosoever therefore shall confess me before men, him will I confess also before my Father who is in heaven.33But whosoever shall deny me before men, him will I also deny before my Father who is in heaven.34Think not that I am come to send peace on earth: I came not to send peace, but a sword.35For I am come to set a man at variance against his father, and the daughter against her mother, and the daughter-in-law against her mother-in-law.36And a man's foes shall be they of his own household.37He that loves father or mother more than me is not worthy of me: and he that loves son or daughter more than me is not worthy of me.38And he that takes not his cross, and follows after me, is not worthy of me.39He that finds his life shall lose it: and he that loses his life for my sake shall find it.40He that receives you receives me, and he that receives me receives him that sent me.41He that receives a prophet in the name of a prophet shall receive a prophet's reward; and he that receives a righteous man in the name of a righteous man shall receive a righteous man's reward.42And whosoever shall give to drink unto one of these little ones a cup of cold water only in the name of a disciple, verily I say unto you, he shall in no wise lose his reward.


import classNames from 'classnames'
import PropTypes from 'prop-types'
import React from 'react'

import styles from 'part:@sanity/components/formfields/default-style'
import DefaultLabel from 'part:@sanity/components/labels/default'
import ValidationStatus from 'part:@sanity/components/validation/status'
import FieldStatus from '../fieldsets/FieldStatus'
import {FieldPresence} from '../presence'

export default class DefaultFormField extends React.PureComponent {
  static propTypes = {
    label: PropTypes.string,
    className: PropTypes.string,
    inline: PropTypes.bool,
    description: PropTypes.string,
    level: PropTypes.number,
    children: PropTypes.node,
    wrapped: PropTypes.bool,
    labelFor: PropTypes.string,
    markers: PropTypes.arrayOf(
      PropTypes.shape({
        type: PropTypes.string
      })
    ),
    presence: PropTypes.any
  }

  static defaultProps = {
    children: undefined,
    className: undefined,
    description: undefined,
    label: undefined,
    labelFor: undefined,
    level: 1,
    inline: false,
    markers: [],
    wrapped: false
  }

  render() {
    const {
      level,
      label,
      labelFor,
      description,
      children,
      inline,
      wrapped,
      className: classNameProp,
      markers,
      presence
    } = this.props

    const levelClass = `level_${level}`

    const className = classNames(
      classNameProp,
      inline ? styles.inline : styles.block,
      styles[levelClass],
      wrapped && styles.wrapped
    )

    return (

          {label && (

                  {label && (
                    <DefaultLabel className={styles.label} level={level}>
                      {label}
                    </DefaultLabel>
                  )}
                  <ValidationStatus markers={markers} />

                {description &&
{description}
}

              <FieldStatus>
                <FieldPresence presence={presence} />
              </FieldStatus>

          )}

{children}

    )
  }
}


Wanting to feel connected to nature is not uncommon and a lot of modern and contemporary houses are designed to fulfill this desire. However, few designs take it as seriously as that of the MeMo House. This is a residence designed in 2016 by BAM! arquitectura. It’s located in Buenos Aires, in Argentina and it only offers a total of 215 square meters of living space.

View in gallery The roof of the house is a garden, making it seem like nature is taking over the architecture

View in gallery The architecture of the house is shaped by the owner’s passion for landscaping

The house occupies a small plot between two existing buildings. Designing a home that could fit here comfortably was challenging enough and to that the client a series of special requests. Given his passion for landscaping and the serious desire to make this a sustainable and environmentally-friendly home, the architects were asked to include as much green space as possible in their design and to preserve and even add greenery to the house is various forms.

View in gallery The house sits on a plot between two existing buildings, with a long and narrow courtyard at the back

View in gallery The swimming pool is positioned at the center of the yard, with greenery growing around it

View in gallery Solar panels are installed on the roof of the house, suggesting a sustainable design approach

In response to these special requests, the architects did a great job at connecting the house to nature and turning it into an eco-friendly retreat. The defining design element of the project is a vertical garden which connects all the floors of the house, covering part of the roof and terrace and then descending into the house alongside a concrete staircase. This way an interior garden was created. The architects framed it with glass walls so it can be admired from all the interior areas of the house.

View in gallery Full-height windows and sliding glass doors open the living spaces to the backyard

In order for this design approach to work, a lot of things had to complement each other perfectly. The exact placement of the house on the site was important and so was its orientation. It was important to capture the maximum amount of sunlight, especially since the house is powered by solar panels on the roof. That’s not the only detail that makes this house sustainable. There’s also the fact that rainwater is used for irrigation throughout.

View in gallery The roof garden descends on the lower levels, forming an interior garden

View in gallery The living area is squeezed between the interior garden and a covered outdoor lounge space

Native plants were chosen for their familiarity with the land and the climate but also because they’re quite resilient and require little water to stay healthy. They grow along the central staircase, adding color and freshness to the whole house and welcoming nature inside. At the same time, the glass box that frames the staircase and garden also brings sunlight inside the house.

View in gallery Vegetation grows alongside the concrete staircase which connects all the floors of the house


/** Process Functions. */
package org.basex.query.func.proc;


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---
abstract: 'We perform a first principles band calculation for a group of quasi-two-dimensional organic conductors $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M$=P, As, Sb, Ta). The *ab-initio* calculation shows that the density of states (DOS) is correlated with the band width of singly occupied (highest) molecular orbital (SOMO), while it is not necessarily correlated with the unit cell volume. The direction of the major axis of the cross section of the Fermi surface lies in the $\Gamma$-B direction, which differs from that obtained by the extended H$\ddot{\rm u}$ckel calculation. Then, we construct a tight-binding model which accurately reproduces the *ab-initio* band structure. The obtained transfer energies give smaller dimerization than in the extended H$\ddot{\rm u}$ckel band. As for the difference of the anisotropy of the Fermi surface, the transfer energies along the inter-stacking direction are smaller than those obtained in the extended H$\ddot{\rm u}$ckel calculation. Assuming spin-fluctuation-mediated superconductivity, we apply random phase approximation (RPA) to a two-band Hubbard model. This two-band Hubbard model is composed of the tight-binding model derived from the first principles band structure and an on-site (intra-molecule) repulsive interaction taken as a variable parameter. The obtained superconducting gap changes sign four times along the Fermi surface like in a $d$-wave gap, and the nodal direction is different from that obtained in the extended H$\ddot{\rm u}$ckel model. Anion dependence of $T_{\rm c}$ is qualitatively consistent with the experimental observation.'
address:
- '$^1$ Institute of Physics, Kanagawa University, Yokohama, Kanagawa 221-8686, Japan'
- '$^2$ Department of Engineering Science, The University of Electro-Communications, Chofu, Tokyo 182-8585, Japan'
- '$^3$ Faculty of Engineering, Hiroshima Institute of Technology, Hiroshima 731-5193, Japan'
- '$^4$ Department of Material Science, University of Hyogo, Ako-gun, Hyogo 678-1297, Japan'
author:
- 'H Aizawa$^1$[^1], K Kuroki$^2$, S Yasuzuka$^3$ and J Yamada$^4$'
title: 'Model construction and superconductivity analysis of organic conductors $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M$=P, As, Sb, Ta) based on first principles band calculation'
---

Introduction {#Introduction}
============

Ever since their discovery, physics and chemistry of organic superconductors have attracted much attention [@Ardavan-Brown-JPSJ-81-011004]. One of the interesting features of these superconductors is the possibility of unconventional pairing arising from electron correlation effects. From this point of view, there have been efforts to control the strength of the electron correlation via chemical modification of molecules, and this has lead to the discovery of several new superconductors [@Yamada-Watanabe-JACS-104-5057]. Among those superconductors, here we focus on a group of organic conductors $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M=$P, As, Sb, Ta), where BDA-TTP is an abbreviation of 2,5-bis(1,3-dithian-2-ylidene)-1,3,4,6-tetrathiapentalene. BDA-TTP molecule is derived from BDH-TTP by stereochemical modification, where BDH-TTP is an abbreviation of 2,5-bis(1,3-dithiolan-2-ylidene)-1,3,4,6-tetrathiapentalene. While BDH-TTP salts show stable metallic behavior suggesting weak electron correlation, the BDA-TTP salts exhibit stronger electron correlation, which is expected from the band width narrowing due to the chemical modification. In fact, $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ exhibit superconductivity with $T_{\rm c}$=7.5, 5.8, 5.9K for $M=$Sb, As, P, respectively [@Yamada-Watanabe-JACS-123-4174], while $M=$Ta does not superconduct [@Yamada-Fujimoto-SM-153-373]. The conducting layer is sandwiched by insulating layers of anion $M$F$_{6}$ as shown in figure \[fig1\](a), from which we may expect these salts to be quasi-two-dimensional. The alignment of the BDA-TTP donors in the conducting layer takes the $\beta$-type configuration shown in figure \[fig1\](b).

![ Lattice structure of $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$: (a) the side view and (b) the top view of the conducting BDA-TTP layer. []{data-label="fig1"}](fig1.eps){width="14.0cm"}

Measurements of Shubnikov-de Haas (SdH) oscillation and angular-dependent magneto-resistance oscillation (AMRO) for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ have shown a two-dimensional Fermi surface [@Choi-Jobilong-PRB-67-174511] , which is consistent with the tight-binding band structure [@Yamada-Watanabe-JACS-123-4174] obtained from the extended H$\ddot{\rm u}$ckel calculation [@Mori-Kobayashi-BCSJ-57-627]. However, a very recent AMRO measurement shows that the direction of the anisotropy of the Fermi surface differs from the previous AMRO measurement, and suggests the direction of the major axis of the cross section lies in the $\Gamma$-B direction of the Brillouin zone (see figure \[fig2\]) [@Yasuzuka-Koga-JPSJ-short-notes]. It is worth mentioning that the effective cyclotron mass takes a large value of $m_{c}^{*}/m_0 = 12.4 \pm 1.1$, which indicates that these materials are strongly correlated electron systems, although the normal state exhibits a metallic nature.

Measurements of the upper critical field ($H_{c2}$) of $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ have shown spin-singlet pairing [@Shimojo-Ishiguro-JPSJ-71-717; @Tanatar-Ishiguro-PRB-71-024531]. The temperature dependence of the electronic specific heat has indicated presence of a nodal structure in the superconducting order parameter [@Shimojo-Ishiguro-JPSJ-71-717], and a scanning tunneling microscope (STM) experiment also suggests presence of anisotropy in the gap, where the nodes (or the gap minima) lie in the $k_{a} \pm k_{c}$ direction [@Nomura-Muraoka-PhysicaB-404-562]. On the other hand, a recent study of the in-plane anisotropy of $H_{\rm c2}$ shows that the $H_{\rm c2}$ maxima appears when the magnetic field is applied in the $k_{a} \pm k_{c}$ direction, i.e., the nodal direction indicated in the STM measurement [@Yasuzuka-Koga-ICSM2010-5Ax-10]. This is puzzling because the $H_{\rm c2}$ maxima usually appears when the field is applied in the antinodal direction. A uniaxial pressure experiment for $M=$As and Sb shows that $T_{\rm c}$ once increases and takes a maximum under the compression parallel to the stacking direction [@Ito-Ishihara-PRB-78-172506].

Theoretically, several studies have adopted the models derived from extended H$\ddot{\rm u}$ckel calculation, and analysis on superconductivity has also been performed assuming spin fluctuation mediated pairing [@Berk-Schrieffer-PRL-17-433; @Moriya-Takahashi-Ueda-JPSJ-59-2905]. Nonoyama [*et al.*]{} [@Nonoyama-Maekawa-JPSJ-77-094703; @comment-Nonoyama-et-al] applied RPA to the two band model for $M=$As and Sb, while Suzuki [*et al.*]{} [@Suzuki-Onari-JPSJ-80-094704] applied the fluctuation exchange (FLEX) approximation to the original two-band model and the single-band dimer model for $M=$As and Sb, and discussed the pressure dependence. There, the $d$-wave like gap function has been obtained, whose nodal direction is consistent with the STM measurement [@Nomura-Muraoka-PhysicaB-404-562], but not with the recent study of in-plane anisotropy of $H_{\rm c2}$ [@Yasuzuka-Koga-ICSM2010-5Ax-10].

Thus, there are several controversies regarding the relation between experiments and theoretical studies based on the extended H$\ddot{\rm u}$ckel model. In the present paper, we study theoretically the organic conductors $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M=$P, As, Sb, Ta) based on a model constructed from [*ab-initio*]{} band calculation based on the density functional theory (DFT) exploiting the WIEN2K package [@WIEN2K]. In fact, the importance of model construction of molecular solids based on [*ab-initio*]{} calculation has recently pointed out in several studies [@Kandpal-Opahle-PRL-103-067004; @Jeschke-Souza-PRB-85-035125; @Nakamura-Yoshimoto-JPSJ-78-083710]. We point out the difference in the band structure and the Fermi surface between the [*ab-initio*]{} (non-empirical method) and the extended H$\ddot{\rm u}$ckel calculations (semi-empirical method), and its consequence to the superconducting gap mediated by spin fluctuations. We also study the anion dependence of the band structure, and how it can affect the superconducting transition temperature.

Method {#Method}
======

[*ab-initio*]{} band calculation and model construction {#First principles band calculation}
-------------------------------------------------------

We perform an [*ab-initio*]{} band calculation using all-electron full potential linearized augmented plane-wave (LAPW) + local orbitals (lo) method within WIEN2K [@WIEN2K]. This implements the DFT with different possible approximation for the exchange correlation potentials. The exchange correlation potential is calculated using the generalized gradient approximation (GGA).

To attain convergence in the eigenvalue calculation, the single-particle wave functions in the interstitial region are expanded by plane waves with a cut-off of $R_{\rm MT} K_{\rm max}=3.0$, where $R_{\rm MT}$ denotes the smallest muffin tin radius and $K_{\rm max}$ is the maximum value of $K$ vector in the plane wave expansion. For $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$, for instance, the muffin-tin radii are taken as 1.74, 1.74, 1.62, 0.83, and 0.45 in atomic units (au) for Sb, F, S, C, and H, respectively. Thus $K_{\rm max}$ is 3/0.45$\approx$6.7, and the plane wave cutoff energy is 604.7 eV. Calculations are performed using 7$\times$3$\times$9 $k$-points in the irreducible Brillouin zone. We adopt the lattice structure determined experimentally (including the coordinates of the H atoms)[@Yamada-Watanabe-JACS-123-4174], and we do not relax the atomic positions in the calculation.

Having done the [*ab-initio*]{} calculation, we then construct a tight-binding model which accurately reproduces the *ab-initio* band structure. From figure \[fig1\](b), it can be seen that the conducting BDA-TTP layer has two BDA-TTP molecules in a unit cell, so we regard one molecule as a site, and consider a two-band (two sites per unit cell) tight-binding model to fit the *ab-initio* band structure. The tight-binding Hamiltonian we consider, $H_{0}$, is written in the form $$\begin{aligned}
 H_{0}=\sum_{\left< i \alpha: j \beta \right>, \sigma}
  \left\{ t_{i \alpha: j \beta}
   c_{i \alpha \sigma}^{\dagger} c_{j \beta \sigma} + {\rm H. c.}
  \right\},
\label{H0ij}\end{aligned}$$ where $i$ and $j$ are unit cell indices, $\alpha$ and $\beta$ specifies the sites in a unit cell, $c_{i \alpha \sigma}^{\dagger}$ ($c_{i \alpha \sigma}$ ) is a creation (annihilation) operator with spin $\sigma$ at site $\alpha$ in the $i$-th unit cell, $t_{i \alpha: j \beta}$ is the electron transfer energy between $(i, \alpha)$ site and $(j, \beta)$ site, and $\left< i \alpha: j \beta \right>$ represents the summation over the bonds corresponding to the transfer.

By Fourier transformation, equation (\[H0ij\]) is rewritten as $$\begin{aligned}
 H_{0}=\sum_{\textbf{\textit k}, \sigma, \alpha, \beta}
  \varepsilon_{\alpha \beta}\left( \textbf{\textit{k}} \right)
   c_{\textbf{\textit k} \alpha \sigma}^{\dagger}
   c_{\textbf{\textit k} \beta \sigma}, \end{aligned}$$ where $\varepsilon_{\alpha \beta}\left( \textbf{\textit{k}} \right)$ is the site-indexed kinetic energy represented in $\textbf{\textit{k}}$-space. The band dispersion is given by diagonalizing $\varepsilon_{\alpha \beta}\left( \textbf{\textit{k}} \right)$, $$\begin{aligned}
 \varepsilon_{\alpha \beta}\left( \textbf{\textit{k}} \right)
  =\sum_{\gamma}
  d_{\alpha \gamma}\left( \textbf{\textit{k}} \right)
  d_{\beta \gamma}^{*}\left( \textbf{\textit{k}} \right)
  \xi_{\gamma}\left( \textbf{\textit{k}} \right),
  \label{eps-ab}\end{aligned}$$ where $\xi_{\gamma}\left( \textbf{\textit{k}} \right)$ is the dispersion of the $\gamma$ band measured from the chemical potential, and $d_{\alpha \gamma}\left( \textbf{\textit{k}} \right)$ is the unitary matrix that gives the transformation.

In order to study unconventional superconductivity, we employ the two-band Hubbard model obtained by adding the on-site (intra-molecule) repulsive interaction to the tight-binding model derived from the [*ab-initio*]{} band structure. The Hubbard Hamiltonian, $H$, is $$\begin{aligned}
 H=H_{0}
  +\sum_{i \alpha} U
  n_{i \alpha \uparrow} n_{i \alpha \downarrow}
  \label{Hij}\end{aligned}$$ where $U$ is the on-site interaction and $n_{i \alpha \sigma}$ is the number operator of the electron on $\alpha$-site in the $i$-th unit cell. The on-site $U$ in the present study is fixed at a certain value. Although this choice does not have a quantitative basis, taking other values of $U$ does not affect qualitatively the conclusion of the present paper regarding the superconducting gap symmetry and the anion dependence of $T_c$. Note also that we ignore the off-site (inter-molecule) repulsive interactions. This is based on the result obtained in a previous theoretical work for the extended H$\ddot{\rm u}$ckel model of the present materials [@Nonoyama-Maekawa-JPSJ-77-094703]. There it has been shown that the introduction of moderate inter-molecule interactions only slightly modifies the position of the nodes of the gap. Although the model adopted here is different, we believe that the effect of the inter-site interaction should be similar as far as the off-site interaction values are moderate.

Random phase approximation and superconducting gap equation {#Random phase approximation and superconducting gap equation}
-----------------------------------------------------------

We apply RPA to the two-band Hubbard model given by equation (\[Hij\]) as follows. The bare susceptibility matrix in the site-representation is given by $$\begin{aligned}
 \chi^{0}_{\alpha \beta} \left(\textbf{\textit{q}} \right)
 &=&\frac{-1}{N} \sum_{ \textbf{\textit{p}} } \sum_{ \gamma, \gamma' }
% \nonumber \\
% & &
  d_{\alpha \gamma}\left( \textbf{\textit{p}}+\textbf{\textit{q}} \right)
  d_{\beta  \gamma}^{*}\left( \textbf{\textit{p}}+\textbf{\textit{q}} \right)
  d_{\beta  \gamma'}\left( \textbf{\textit{p}} \right)
  d_{\alpha \gamma'}^{*}\left( \textbf{\textit{p}} \right)
  \nonumber \\
 & &\times
   \frac{ f\left[ \xi_{\gamma} \left( \textbf{\textit{p}}+\textbf{\textit{q}} \right) \right]
         -f\left[ \xi_{\gamma'}\left( \textbf{\textit{p}} \right) \right] }
        { \xi_{\gamma} \left( \textbf{\textit{p}}+\textbf{\textit{q}} \right)
         -\xi_{\gamma'}\left( \textbf{\textit{p}} \right) },
 \label{chi0}\end{aligned}$$ where $N$ is the total number of unit cells, and $f\left( \xi \right)$ is the Fermi distribution function (this is the multi-site version of the Lindhard function). The indices $\alpha\beta$ on the left hand side means ($\alpha$, $\beta$)-element of the bare susceptibility matrix $\hat{{X}}^{0}$. Within RPA, the spin and charge susceptibilities are obtained as $$\begin{aligned}
 \hat{{X}}^{\rm sp}
  &=&\left( \hat{I}-\hat{{X}}^{0} \hat{U} \right)^{-1} \hat{{X}}^{0},
  \label{chisp}
  \\
 \hat{{X}}^{\rm ch}
  &=&\left( \hat{I}+\hat{{X}}^{0} \hat{U} \right)^{-1} \hat{{X}}^{0},
  \label{chich}\end{aligned}$$ respectively. $\hat{{X}}^{\rm sp}$, $\hat{{X}}^{\rm ch}$, $\hat{{X}}^{0}$ are the spin, charge, and bare susceptibility matrices, respectively, $\hat{U}$ is the on-site interaction matrix, and $\hat{I}$ is the unit matrix. In a two-band system, $\hat{U}$, $\hat{X}^{0}$, $\hat{X}^{\rm sp}$ and $\hat{X}^{\rm ch}$ all become 2$\times$2 matrices. The “spin susceptibility” (see figure \[fig7\](a)) in the present paper is obtained as the larger eigenvalue of the 2$\times$2 spin susceptibility matrix. By using these susceptibility matrices, the pairing interaction $\hat{V}^{\rm singlet}$ for the spin-singlet state is given as $$\begin{aligned}
 \hat{V}^{\rm singlet}
  &=& \hat{U}
     +\frac{3}{2}\hat{U}\hat{{X}}^{\rm sp}\hat{U}
     -\frac{1}{2}\hat{U}\hat{{X}}^{\rm ch}\hat{U}.
  \label{pairing-int}\end{aligned}$$ Using the pairing interaction given by equation (\[pairing-int\]), we solve the linearized gap equation to obtain the transition temperature $T_{\rm c}$ and the superconducting gap function for the spin-singlet pairing state. The linearized gap equation within the weak-coupling theory is given by $$\begin{aligned}
 \lambda \varphi_{\alpha \beta} \left( \textbf{\textit{k}} \right)
  &=&
  \frac{-1}{N}\sum_{ \textbf{\textit{k}}' }\sum_{\alpha' \beta'}\sum_{\gamma \gamma'}
  V^{\rm singlet}_{\alpha \beta} \left( \textbf{\textit{k}}-\textbf{\textit{k}}' \right)
  \nonumber \\
  &\times&
  d_{\alpha  \gamma }    \left( \textbf{\textit{k}}' \right)
  d_{\alpha' \gamma }^{*}\left( \textbf{\textit{k}}' \right)
  d_{\beta   \gamma'}    \left(-\textbf{\textit{k}}' \right)
  d_{\beta'  \gamma'}^{*}\left(-\textbf{\textit{k}}' \right)
  \nonumber \\
  &\times&
  \frac{ -f\left[ \xi_{\gamma } \left( \textbf{\textit{k}}' \right) \right]
         +f\left[-\xi_{\gamma'} \left(-\textbf{\textit{k}}' \right) \right]}
       { \xi_{\gamma }\left( \textbf{\textit{k}}' \right)
        +\xi_{\gamma'}\left(-\textbf{\textit{k}}' \right)}
    \varphi_{\alpha' \beta'}\left( \textbf{\textit{k}}' \right),
  \label{gap-eq}\end{aligned}$$ where $\lambda$ is the eigenvalue of the linearized gap equation, and $\varphi_{\alpha \beta}\left( \textbf{\textit{k}} \right)$ is the ($\alpha$, $\beta$)-element of the gap function matrix. The transition temperature $T_{\rm c}$ is the temperature where $\lambda$ reaches unity. In a two-band system, $\hat{V}^{\rm singlet}$ and $\hat{\varphi}$ become 2$\times$2 matrices.

Although RPA is quantitatively insufficient for evaluating the absolute value of $T_{\rm c}$, we expect this approach to be valid for (i) studying the form of the superconducting gap function assuming spin-fluctuation-mediated pairing, and (ii) qualitatively comparing the tendency toward superconductivity (or $T_c$) between the different anions. We take 128$\times$128 $k$-point meshes in the RPA calculation throughout the entire study.

Results {#Results}
=======

[*ab-initio*]{} band calculation {#First principles band calculation}
--------------------------------

We show in figure \[fig2\](a) the *ab-initio* band structure for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ at ambient pressure and room temperature.

![ (a) Calculated *ab-initio* band structure, (b) the density of states, and (c) the Fermi surface of $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ at ambient pressure and room temperature, where X(Z)-axis corresponds to the $a$($c$)-direction in the lattice structure. In figure (a), the red curve represent the *ab-initio* band dispersions and the blue solid curves gives the tight-binding fit. []{data-label="fig2"}](fig2.eps){width="10.0cm"}

It can be seen that the singly occupied (highest) molecular orbital (SOMO) and the highest-occupied molecular orbital (HOMO) near the Fermi level (zero energy) are isolated from other bands, although there are two bands somewhat close to the HOMO band, which correspond to HOMO$-$1 and HOMO$-$2. Density of states (DOS) in figure \[fig2\](b) also shows the isolation of the HOMO and SOMO from the other bands. From these results, it can be considered that the SOMO and HOMO bands are the target bands to construct a low energy tight-binding model. figure \[fig2\](c) shows the Fermi surface of the *ab-initio* calculation, where the name of the $k$-points are presented only on the $k_{\rm Y} (k_{b})=0$ plane, e.g $\Gamma$=(0, 0, 0), Z=(0, 0, $\pi$/c ) and B=($\pi$/a, 0, $-\pi$/c ). We also show similar plots for $\beta$-(BDA-TTP)$_{2}$AsF$_{6}$ at ambient pressure and room temperature in figure \[fig3\].

![ Plots similar to Fig\[fig2\] for $\beta$-(BDA-TTP)$_{2}$AsF$_{6}$ at ambient pressure and room temperature ; (a) Calculated *ab-initio* band structure, (b) the density of states, and (c) the Fermi surface. []{data-label="fig3"}](fig3.eps){width="10.0cm"}

The band structure and the Fermi surface are similar between the two salts. $M=$P and Ta also give similar results (not shown). The DOS also looks similar qualitatively, but its quantitative dependence on the anions will be discussed later.

The Fermi surface is clearly cylindrical, reflecting the strong two dimensionality of this salt. The direction of the anisotropy of the Fermi surface differs from that found in the previous extended H$\ddot{\rm u}$ckel calculation [@Yamada-Watanabe-JACS-123-4174; @Yamada-Fujimoto-SM-153-373; @Nonoyama-Maekawa-JPSJ-77-094703; @Suzuki-Onari-JPSJ-80-094704]. The origin of this difference is intimately related to including/excluding the 3d-orbital of the sulfur atoms of the TTP skeleton donors in the extended H$\ddot{\rm u}$ckel calculation [@Ouyang-Yakushi-JPSJ-67-3191; @Kawamoto-Ashizawa-JPSJ-71-3059; @Drozdova-Yakushi-JSSC-168-497]. Actually, the shape of the Fermi surface given by the extended H$\ddot{\rm u}$ckel calculation in which the 3d-orbital of the sulfur atoms is excluded [@Kawamoto-private-comm-3d] is similar to the present *ab-initio* result. Focusing on the comparison of the experiments with our results of the Fermi surface, the anisotropy of the Fermi surface differs from the previous experiment [@Choi-Jobilong-PRB-67-174511], but a very recent AMRO measurement shows that the long-axis of the Fermi surface ellipse is in the $\Gamma$-B direction, which is at least qualitatively consistent with the present result [@Yasuzuka-Koga-JPSJ-short-notes]. However, the size of the Fermi surface is not consistent between this experiment and the present calculation, and this remains as a puzzle.

Now, one of the important issues we study in the present paper is the effect of substituting the anion. Here we consider the anion dependence of the band-width and the DOS at the Fermi level for $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M$=P, As, Sb, Ta) at ambient pressure and room temperature, and also for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ at 12K. As for the band width, we introduce $W_{\rm SH}$ and $W_{\rm SOMO}$, where the former is the energy difference between the top of SOMO and the bottom of HOMO, and the latter is the band width of SOMO alone.

![ (a) SOMO+HOMO band width, (b) SOMO band width, and (c) the density of states against the unit-cell volume. LT in parentheses for Sb means that the low temperature lattice parameters are used. The inset of (b) shows the schematic relation between SOMO and HOMO. []{data-label="fig4"}](fig4.eps){width="11.0cm"}

figure \[fig4\](a) shows that $W_{\rm SH}$ becomes smaller as the anion is enlarged from $M=$P to Sb, resulting in an increase of the unit-cell volume. The trend can naturally be understood as the effect of the chemical pressure. $M=$Ta, however, is an exception, where the increase of the unit-cell volume from $M=$Sb results in an increase in the band width. The relation between $M=$Sb and $M=$Sb(LT) shows that lowering the temperature results in an increases of $W_{\rm SH}$ due to thermal compression. We show in figure \[fig4\](b) $W_{\rm SOMO}$ against the unit-cell volume. The correlation between $W_{\rm SOMO}$ and the volume is not monotonic in contrast to the volume dependence of $W_{\rm SH}$, even within the pnictogens $M=$P, As and Sb. The reason for this lies in the small dimerization gap between the SOMO and HOMO bands. Even though $W_{\rm SOMO}$ of $M=$As is larger than that of $M=$P, $W_{\rm SH}$ of As is smaller because the dimerization gap of As is smaller than that of P. A schematic figure is shown in the inset of figure \[fig4\](b), where the left (right) figure corresponds to $M=$P (As). We will come back to this point in the next subsection. The volume dependence of the DOS at the Fermi level, DOS($E_{\rm F}$), varies in accord with $W_{\rm SOMO}$, not $W_{\rm SH}$, as seen in figure \[fig4\](c). It is natural that DOS is inversely related to $W_{\rm SOMO}$ because this directly measures the width of the band that intersects the Fermi level, but the point here is that $W_{\rm SOMO}$ is not directly correlated with $W_{\rm SH}$ and thus the unit cell volume.

Effective tight-binding model {#Effective model}
-----------------------------

Figure \[fig5\] shows the effective tight-binding model adopted to fit the *ab-initio* band. In addition to the nearest-neighbor transfer energies (left part in figure \[fig5\], same notation is used as in previous studies), we need to introduce the next-nearest-neighbor transfer energies (right panel in figure \[fig5\]) to reproduce the *ab-initio* band more accurately. Note that the stacking direction of the BDA-TTP molecules is taken in the $c+a$-direction of the lattice structure in our study, as shown in figure \[fig1\](b).

![ The tight-binding model adopted to fit the *ab-initio* band structure, where an ellipse corresponds to a BDA-TTP molecule. []{data-label="fig5"}](fig5.eps){width="11.0cm"}

We show in figure \[fig6\](a) the band structure of the two band tight-binding model for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ superposed to the *ab-initio* band structure. It can be seen that the tight-binding model nicely reproduces the *ab-initio* band structure. figure \[fig6\](b) shows the Fermi surface obtained from the model, which is essentially the same as the *ab-initio* result in figure \[fig2\](c).

![ Blue solid curves represent the band structure of the tight-binding model which is fit to the *ab-initio* band (red diamonds) of $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ at room temperature. []{data-label="fig6"}](fig6.eps){width="12.0cm"}

Similar tight-binding fit is performed for all the anions, and the thereby determined transfer energies are summarized in Table \[tab1\]. The bottom two lines of Table \[tab1\] represent the magnitude of the dimerization, $t_{p1}/t_{p2}$, in the stacking direction, and the relative transfer perpendicular to that direction (i.e. the strength of the two dimensionality), $(t_{q1}+t_{q2})/(t_{p1}+t_{p2})$.

  $M$F$_{6}$                               SbF$_{6}$ (LT)   PF$_{6}$   AsF$_{6}$   SbF$_{6}$   TaF$_{6}$
  --------------------------------------- ---------------- ---------- ----------- ----------- -----------
  $t_{p1}$ (eV)                                -0.171        -0.176     -0.162      -0.153      -0.166
  $t_{p2}$                                     -0.155        -0.141     -0.149      -0.126      -0.138
  $t_{q1}$                                     -0.070        -0.065     -0.066      -0.055      -0.061
  $t_{q2}$                                     -0.082        -0.082     -0.071      -0.071      -0.083
  $t_{c }$                                     0.009         0.003       0.008       0.007       0.004
  $t_{2c}$                                     0.008         0.006       0.005       0.005       0.006
  $t_{2p}$                                     0.017         0.015       0.018       0.021       0.015
  $t_{a }$                                    -0.0002        -0.002      0.002       0.003      -0.001
  $t_{2q}$                                     0.007         0.006       0.007       0.005       0.006
  $t_{q3}$                                     0.005         -0.002      0.006       0.003      -0.002
  $t_{q4}$                                     0.005         0.006       0.003       0.006       0.009
  $t_{r1}$                                     0.014         0.015       0.012       0.014       0.016
  $t_{r2}$                                     0.015         0.008       0.011       0.008       0.008
  $t_{p1}/t_{p2}$                               1.10          1.25       1.09        1.21        1.20
  $\frac{t_{q1}+t_{q2}}{t_{p1}+t_{p2}}$        0.466         0.464       0.441       0.452       0.474

  : List of the transfer energies in the unit of eV for $\beta$-(BDA-TTP)$_{2}M$F$_{6}$, where LT means a structural data measured in low temperature.

\[tab1\]

We can now quantitatively discuss the effect of the dimerization on the unit-cell volume dependence of $W_{\rm SOMO}$ and DOS($E_{\rm F}$). Table \[tab1\] shows that $t_{p1}/t_{p2}$ obtained by using the structural data at room temperature is around 1.22 except for $M=$As, in which $t_{p1}/t_{p2}$ is 1.09. This means that the dimerization gap between the SOMO and HOMO bands is small in As, hence resulting in a larger $W_{\rm SOMO}$ despite the smaller $W_{\rm SH}$. This is consistent with the qualitative discussion given in subsection \[First principles band calculation\]. From the viewpoint of the transfer energies, we consider that the difference of the anisotropy of the Fermi surface is due to the magnitude of the two-dimensionality, $(t_{q1}+t_{q2})/(t_{p1}+t_{p2})$. Our result shows that the average value of $(t_{q1}+t_{q2})/(t_{p1}+t_{p2})$ over the salts listed in Table \[tab1\] is around 0.46, which is smaller than that obtained by the extended H$\ddot{\rm u}$ckel calculation [@Yamada-Watanabe-JACS-123-4174; @Yamada-Fujimoto-SM-153-373; @Nonoyama-Maekawa-JPSJ-77-094703; @Suzuki-Onari-JPSJ-80-094704]. Therefore, the present Fermi surface exhibits an anisotropy in which the $a+c$-direction is more conductive than in the extended H$\ddot{\rm u}$ckel result.

Random phase approximation and the superconducting gap equation {#Random phase approximation and superconducting gap equation}
---------------------------------------------------------------

We now move on to the RPA analysis for the effective models. To focus on the anion dependence, here we concentrate on the models obtained using the lattice parameters at room temperature. We show in figure\[fig7\](a) the spin susceptibility in the Hubbard model of $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$, where $U=0.38$\[eV\] and the temperature $T=0.008$\[eV\] here. The wave vector at which the spin susceptibility is maximized is $ \textbf{\textit{k}}=\left( 0.45 \pi, 0.53 \pi \right)$. The arrows in figure\[fig7\](b) corresponds to the peak position of the spin susceptibility in (a), which can be considered as the nesting vector of the Fermi surface. In fact, there is a certain overlap between the original Fermi surface and the ones translated by these arrows, as shown in figure \[fig7\](d).

![ (a) The calculated spin susceptibility. (b) Arrows correspond to the peak position wave vector of the spin susceptibility (nesting vector of the Fermi surface). (c) Spin singlet superconducting gap function of the model for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$, where $U=0.38$, $T=0.008$ in 128$\times$128. For this parameter set, the obtained $\lambda$ is 0.923. (d) The relation between the nesting vector of the Fermi surface and the spin susceptibility. []{data-label="fig7"}](fig7.eps){width="15.5cm"}

The superconductivity is analysed by solving the linearized gap equation that takes into account the pairing interaction mediated by the spin fluctuations. The superconducting gap function of the spin-singlet pairing in figure \[fig7\](c) shows that the sign of the gap changes four times along the Fermi surface like in a $d$-wave gap. Considering that the $\Gamma$-B direction corresponds to the $a-c$ direction in the lattice structure, the obtained gap function indicates that the hot spots are present in the $k_{a} \pm k_{c}$ direction. The position of the nodes is different from those obtained in previous theoretical studies that adopt extended H$\ddot{\rm u}$ckel models (see the appendix) [@Nonoyama-Maekawa-JPSJ-77-094703; @comment-Nonoyama-et-al; @Suzuki-Onari-JPSJ-80-094704], and hence is not consistent with the STM study [@Nomura-Muraoka-PhysicaB-404-562]. On the other hand, the present result is indeed more consistent with the recent measurement of the anisotropy of $H_{\rm c2}$ in $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ [@Yasuzuka-Koga-ICSM2010-5Ax-10]. Further study is necessary to resolve the consistency between existing experiments and theories.

$T_{\rm c}$ is obtained for the four anions for various on-site interaction $U$. figure \[fig8\] shows $T_{\rm c}$ as functions of the unit-cell volume.

![ $T_{\rm c}$ within RPA method for various on-site interaction as a function of the unit-cell volume for $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M$=P, As, Sb, Ta) of ambient pressure. []{data-label="fig8"}](fig8.eps){width="11.0cm"}

There are several features found in the calculation results: (i) $T_c$ is the highest for Sb, (ii) $T_c$ somewhat decreases as we go from P to As, and (iii) $T_c$ goes down as we go from Sb to Ta, but it is still finite, close to that of P. These features are in accord with the anion dependence of DOS($E_{\rm F}$) or $W_{\rm SOMO}$ shown in Fig \[fig4\](c) or (b), but not $W_{\rm SH}$ or the unit-cell volume. Point (i) is indeed consistent with the experimental finding. Point (ii) can also give an understanding for the experimental observation that $T_c$ does not increase substantially as we go from P to As. This may at first sight be puzzling from the viewpoint of the increase in the unit-cell volume, from which one would expect an increase in the density of states. The key for the present understanding is the difference in the strength of the dimerization between P and As as mentioned previously. As for point (iii), $T_c$ of Ta being somewhat close to P, is not consistent with the experiments, where no superconductivity is observed for Ta. The discrepancy may be due to effects that are not taken into account in the present model (such as phonons), or in the RPA (more sophisticated electron correlation effects). On the other hand, the decrease of the $T_c$ with the increase of the unit-cell volume found in the present calculation might partially be related to the loss of superconductivity.

Conclusion {#Conclusion}
==========

In the present paper, we have obtained the *ab-initio* band structure and the effective tight-binding model of $\beta$-(BDA-TTP)$_{2}M$F$_{6}$ ($M=$P, As, Sb, Ta), and studied the superconducting gap form as well as the anion dependence of $T_c$ assuming spin fluctuation mediated pairing.

The results of *ab-initio* band calculation for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ show that the direction of the major axis of the cross section of the Fermi surface lies in the $\Gamma$-B direction, in contrast to the extended H$\ddot{\rm u}$ckel result. The density of states at the Fermi level is correlated with the band width of SOMO rather than SOMO+HOMO, and hence is not necessarily correlated with the unit-cell volume.

To construct an effective tight-binding model that accurately reproduces the *ab-initio* band structure, we need both nearest and next nearest neighbor transfer energies. From the obtained transfer energies, the dimerization of $M=$As is smaller than that of $M=$P and Sb, and hence the SOMO band width of $M=$P is smaller than that of $M=$As despite the larger SOMO+HOMO band width.

The RPA calculation shows that the wave vector at which the spin susceptibility is maximized lies in the $a+c$ direction. The gap function of the superconductivity mediated by the spin fluctuations changes sign along the Fermi surface like in a $d$-wave gap, and the hot spots of the gap (gap maxima) is in the $k_{a} \pm k_{c}$ direction, again different from the extended H$\ddot{\rm u}$ckel model. $T_{\rm c}$ of $M=$Sb is the highest among all the anions in qualitative agreement with experiments.

There are some remaining issues that should be resolved in future studies. As mentioned above, the relation between the present Fermi surface, those obtained by extended H$\ddot{\rm u}$ckel calculation [@Yamada-Watanabe-JACS-123-4174; @Yamada-Fujimoto-SM-153-373; @Nonoyama-Maekawa-JPSJ-77-094703; @Suzuki-Onari-JPSJ-80-094704], and those obtained in two experiments [@Choi-Jobilong-PRB-67-174511; @Yasuzuka-Koga-JPSJ-short-notes] remains as an open question. As for the band calculation, we consider that the difference between the present [*ab-initio*]{} result and the extended H$\ddot{\rm u}$ckel result is intimately related to the empirical parameter in the extended H$\ddot{\rm u}$ckel calculation that controls including/excluding the 3d-orbital of the sulfur atoms of the TTP skeleton donors [@Ouyang-Yakushi-JPSJ-67-3191; @Kawamoto-Ashizawa-JPSJ-71-3059; @Drozdova-Yakushi-JSSC-168-497]. Actually, the extended H$\ddot{\rm u}$ckel result in which the 3d-orbital of the sulfur atoms is excluded [@Kawamoto-private-comm-3d] is similar to the present *ab-initio* result. Although all experimental and theoretical studies suggest anisotropic superconducting gap, the form of the gap function is different between the present and previous theoretical studies based on extend H$\ddot{\rm u}$ckel band [@Nonoyama-Maekawa-JPSJ-77-094703; @Suzuki-Onari-JPSJ-80-094704]. Given the consistency between the recent experiment[@Yasuzuka-Koga-JPSJ-short-notes] and the present calculation regarding the direction of the anisotropy of the Fermi surface, we believe that the gap maxima should lie in the $k_{a} \pm k_{c}$ direction [*as far as the spin-fluctuation-mediated pairing mechanism is concerned*]{}. If the nodes of the superconducting gap do not lie in this direction in the actual materials, then the present study would conversely suggest that a different pairing mechanism may be at work. In this sense, it is highly important to resolve the experimental controversy regarding the direction of the nodes in the superconducting gap [@Nomura-Muraoka-PhysicaB-404-562; @Yasuzuka-Koga-ICSM2010-5Ax-10].

We acknowledge T. Kawamoto, M. Tsuchiizu, A. Kobayashi, Y. Suzumura, and K. Nomura for valuable discussions. This work is supported by Grant-in-Aid for Scientific Research from the Ministry of Education, Culture, Sports, Science and Technology of Japan, and from the Japan Society for the Promotion of Science. Part of the calculation has been performed at the facilities of the Supercomputer Center, ISSP, University of Tokyo.

Spin susceptibility and pairing symmetry in the model based on the extended H$\ddot{\rm u}$ckel band {#Appendix}
====================================================================================================

In this appendix, we show the calculation result obtained by applying the same RPA method to the Hubbard model based on the extended H$\ddot{\rm u}$ckel band. Although the present result is essentially the same as those obtained in previous studies [@Nonoyama-Maekawa-JPSJ-77-094703; @comment-Nonoyama-et-al; @Suzuki-Onari-JPSJ-80-094704] here we show the results in the same manner as in figures \[fig7\] to make the comparison clearer. Here, we concentrate on the model for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ [@Yamada-Watanabe-JACS-123-4174]. The parameter values are $U=0.34$\[eV\] and $T=0.008$\[eV\].

![ (a) The calculated spin susceptibility. (b) Spin singlet superconducting gap function of the extended model H$\ddot{\rm u}$ckel for $\beta$-(BDA-TTP)$_{2}$SbF$_{6}$ with $U=0.34$, $T=0.008$ in 128$\times$128. For this parameter set, the obtained $\lambda$ is 0.997. (c) The relation between the superconducting gap sign change and the spin fluctuations. The dashed arrows connect the portions of the Fermi surface that have the maximum gap with different signs. []{data-label="fig9"}](fig9.eps){width="15.5cm"}

The calculated spin susceptibility is shown in figure \[fig9\](a). It can be seen that it has a broad maximum around the B point, indicating that there is no well defined nesting for this Fermi surface. The spin-singlet superconducting gap function in figure \[fig9\](b) shows that the sign of the gap changes four times along the Fermi surface, but the direction of the nodes differs from that of the *ab-initio* band model shown in figure \[fig7\](c). If we consider a wave vector that connects the two gap maxima positions on the Fermi surface with different signs of the gap, the vector falls on the broad maximum area in the spin susceptibility as shown in figure\[fig9\](c), indicating that the sign change is indeed due to the repulsive pairing interaction mediated by the spin fluctuations. We note that the direction of the nodes obtained for this model is in the $k_{a} \pm k_{c}$ direction, which is in agreement with the STM measurement [@Nomura-Muraoka-PhysicaB-404-562], but not with the in-plane anisotropy of $H_{\rm c2}$ [@Yasuzuka-Koga-ICSM2010-5Ax-10].

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[^1]: Author to whom any correspondence should be addressed


Our Strategies work regardless of market direction or economic conditions.

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The Florence Cathedral, or Duomo of Florence (Not referring to the large Dome at the top of the Basilica, but actually a general term for cathedrals in Italy, e.g. Domus or House of God), is a an amazing site, and a must-see on any trip to Florence. I would say that the visit rivals that of St. Peter's Basilica in Rome, since you can literally climb to the top of the Dome, viewing the painted Dome up close, and taking panoramic views of the whole city of Florence.

The trip is actually to three different buildings, the climb up the dome, and down to the Museum below the cathedral. The Cathedral is a visit similar to other Basilicas/Cathedrals, where you walk around. The real cool visits are climbing up the Dome, as well as the climb up the free standing bell tower, Giotto's Campanile.

The first climb up the Dome shows you the internal Dome. You can look down at the cathedral and up at the amazing dome!

Down there are some plexi-glass protectors that obstruct the view a little, but not so bad.

Above you can see the magnificent fresco painted on the internal part of the dome, depicting the last judgement.

Then you go up some more stairs to get to the top of the dome...

You can see some teasers as you climb!

It's pretty cool to be able to climb up these things...

It's important to not write on the walls...Huai danmen! Central country people are so bad!Eventually it starts to get rounded and you see bricks!A port-hole for when the river Arno periodically floods...You finally get up some curvy stairs...

And you can see the whole of Florence!!!

Also the Santa Maria Novella and the Basilica of San Lorenzo to the west.

Towards the Old Palace and the Piazza della Signoria:

As you come back down you can see a small exhibit on how the dome was built:

Up the bell tower you can get some nice shots of the dome and cathedral:

The whitewashed walls seem plain compared to the dome and marble polychrome exterior:

You can get some perspective snaps of the internal dome, farther away:

There are lots of stained-glass windows:

It's hard to even read what the letters are!

Also there is the baptistery that you can see at the Duomo, but unfortunately it was closed for construction during fall 2014 when we were there.

I hope you enjoyed this post! Follow me to see more-- next week we're going to the picturesque villages of the Cinque Terre (21st of Jan. 2015)!

Consider following my posts on Facebook, it would make my day! I try to post once a week... next week, I'm making a post about the Cinque Terre!You can really get up close to the fresco, which took 11 years to paint.You can see some of the great creepiness of the Capital Sins and Hell:Three main artists worked on the fresco, supported with many aids.You can see an octagonal oculus of the brick dome as well.You can see the bell tower:The Basilica of Santa Croce and the Palazzo Vecchio are in the distance:The Basilica of Santa Croce with it's marble facade:The Santa Maria Novella is both a train station and cathedral:You are pretty free at the top:They didn't use a wood support structure of this dome, which was a first in Italy.You have a full 24 hrs to see all of the five sites, the Cathedral, The Dome, The Bell Tower, The Museum and the Baptistery. The next most inspiring is up the bell tower, Giotto's Campanile.It's made of impressive polychrome marble:Also you can see some creepy heights:Less high than the dome, you can get some shots of the city at different perspectives:The tiled roofs are quite pretty:Here's the palazzo Vecchio tower:You can also see details of the basilica:And look down as you stand on a grid:The dome is quite beautiful from here:You can also enter the cathedral and museum. The cathedral visit is similar to other cathedrals (unless you know something about the art, but we didn't research anything beforehand, so for us it wasn't as exciting as the breathtaking views of the dome and the campanile.Impressive details abound:The clock is interesting since it goes the full 24 hrs in one spin.Downstairs you can see the museum:There you can see some of the recovered older parts of the cathedral that were built upon.There are some impressive tiled floors:Some tombstones are possible to view, but in general the museum was still under construction as of fall 2014.


A blog that showcase all latest New Launches & Property Launches in Singapore & Overseas. For more information, visit https://www.newlaunchonline.com.sg

Friday, May 16, 2014

Alex Residences at Redhill

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Amidst the peace of the haven, the pleasure of urban area existence remains close within reach. Alex Residences is located within an established residential property and a brief 10 minutes’ drive to Orchard Road, the Central Business District, Marina Bay as well as the Southern Waterfront area exactly where Vivocity and Sentosa are located.

Alex Residences is additionally situated within a brief walking length towards the Redhill MRT station, future residents will love convenient access to any or all parts of Singapore through the MRT method. The future residential development can also be nicely hooked up to significant arterial roadways and expressways such as for instance Alexandra Road, Tanglin Road and Ayer Rajah Expressway. At Alex Residences, the connection to modern conveniences is only a train ride away, while amenities close by meet your day-to-day requirements.

The compact condo unit layout was designed to accommodate to boutique lifestyle that fits the special needs for small household and young professionals and the well travelled Singaporeans. The “hotel” like concept facilities tend to be distributed from the floor to the sky with 3 level of sky terraces that offers work, play and relax facilities, a concept to make Alex Residences complete as a boutique condo. The most spectacular one is roof top terrace situated at the 40th floor of this development , which offers panoramic view of Singapore’s northern botanical greeneries, the southern coast line together with famous city skyline. In addition it provides an impressive 25m by 7m air pool , a spa pool, an air lounge and a multi-purpose area so that you could chill out your mind after every day of busy routine.

With an ideal location and good surroundings, Alex Residences is outstanding investments for investors. Alex Residences symbolizes class, grandeur, in one time, progress. This high-rise luxurious condo tower function all the amenities, facilities, and solutions that any person would want and need in a holiday accommodation. Depending on your preferences, you can choose from a variety of diverse units from single bedroom units to luxurious 3 bedroom plus utility.

For parents-to-be or parents looking for reliable school to enrol their child, the much sought after Gan Eng Seng Primary School is actually very well situated within 1 km of Alex Residences.