# ’Checkerboard stripe’ electronic state on cleaved surface of NdO0.7F0.3BiS2
probed by scanning tunneling microscopy

T. Machida1, Y. Fujisawa1, M. Nagao2,3, S. Demura3, K. Deguchi3, Y. Takano3
and H. Sakata1 1Department of Physics, Tokyo University of Science, 1-3
Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
21University of Yamanashi, 7 -32 Miyamae, Kofu 400-8511, Japan
3National Institute for Materials Science, 1-2-1 Sengen, Tsukuba, Ibaraki
305-0047, Japan

###### Abstract

We present scanning tunneling microscopy measurements on a cleaved surface of
the recently discovered superconductor NdO0.7F0.3BiS2 with a transition
temperature ($T_{\mathrm{c}}$) of 5.1 K. Tunneling spectra at 4.2 K (below
$T_{\mathrm{c}}$) and 22 K (above $T_{\mathrm{c}}$) show a large spectroscopic
gap ($\sim$40 mV), which is inconsistent with the metallic nature demonstrated
in bulk measurements. Moreover, we find two interesting real-space electronic
features. The first feature is a ‘checkerboard stripe’ electronic state
characterized by an alternating arrangement of two types of nanocluster. In
one cluster, one-dimensional electronic stripes run along one Bi-Bi direction,
whereas, in the other cluster, the stripes run along the other Bi-Bi
direction. The second feature is a nanoscale electronic inhomogeneity whose
microscopic source seems to be atomic defects on the cleaved surface or dopant
F atoms.

In recent decades, several layered compounds have generated much sustained
interest, because of their peculiar phenomena. An example of these phenomena
is charge-density-wave (CDW) formation in the transition metal
dichalcogenidesDEMoncton ; MNaito ; ASoumyanarayanan ; BSipos ; LJLi ; JJKim ;
RAng  and trichalcogenidesNRu ; HJKim , in which the superconductivity (SC)
often coexists with the CDWDEMoncton ; MNaito ; ASoumyanarayanan ; BSipos ;
LJLi ; JJKim ; RAng . Because of the coexistence of CDW and SC, these
materials are important for understanding the interplay between these
phenomenaBSipos ; LJLi ; RAng . Another example is the high-temperature
superconductivity in copper oxidesBednorz  and iron-pnictidesKamihara . The
superconductivity in these materials often coexists with or emerges in the
proximity of some electronic ordered statesSAKivelson ; CVParker ; MJLawler ;
AMesaros ; YKohsaka ; TMChuang ; SKasahara , which break the $C_{4}$-symmetry
of the underlying crystal lattice. Explorations of the relation between SC and
the electronic ordered states have offered interesting information for
understanding of the mechanisms of unconventional superconductivity.

The recent discovery of BiS2-based superconductors has triggered many research
activities, because of (i) the structural similarity to cuprates and pnictides
and (ii) their relatively high $T_{\mathrm{c}}$Mizuguchi_1 ; SK_Singh ;
Mizuguchi_2 ; JXing ; RJha_1 ; Demura ; MNagao ; XLin ; DYazici . Recent
theoretical calculations have suggested that a quasi-one-dimensional character
of the band dispersion provides a good Fermi surface nestingUsui ; XWan ;
TYildirim ; BLi ; GBMartins . Some of them have proposed that an unstable
phonon at $\boldmath{q}$ = (q, q, 0) corresponding to the Fermi surface
nesting vector causes a CDW instabilityXWan ; TYildirim . How the SC is
related to this Fermi surface nesting has been argued vigorouslyUsui ; XWan ;
TYildirim ; BLi ; GBMartins ; YGao ; YYang ; JLee . Meanwhile, the symmetry of
the superconducting gap has also been investigated theoretically and
experimentally. These studies have suggested the isotropic $s$-, anisotropic
$s$-, and $d$-wave symmetries as possible pairing symmetriesShruti ; GLamura ;
YGao . Despite these studies described above, there is less conclusive
empirical evidence for determining the pairing symmetry and for uncovering
whether CDW instability occurs.

One of the powerful techniques for addressing directly these issues is a
scanning tunneling spectroscopy (STS) using a scanning tunneling microscopy
(STM), which has been used to determine the pairing symmetries in a large
variety of superconductorsRev_Fischer ; Rev_Hoffman ; KMcElroy ; Hanaguri ;
MPAllan . Additionally, this technique has made a significant contribution not
only to visualize the CDW ASoumyanarayanan ; JJKim  and other electronic
ordered statesCVParker ; MJLawler ; YKohsaka ; TMChuang  but also to
disentangle the relationship between the superconductivity and the electronic
ordered states.

Figure 1:  (Color online) (a) A typical STM image on a 240 $\times$ 240 Å2
field of view (FOV) taken at $V_{\mathrm{s}}$ = +500 mV and $I_{set}$ = 500
pA. The inset illustrates a schematic figure of the crystal structure, where
red, gray, yellow, and blue spheres represent Nd, O, S, and Bi atoms,
respectively. (b) A magnified STM image on a 45 $\times$ 45 Å2 FOV. (c) A
Fourier transform image of (a). Red circles indicate the spots corresponding
to the atomic array. Yellow ellipsoids mark the tails corresponding to the
dark streaks running along the diagonal (110) direction of the unit cell. (d)
Typical tunneling spectra taken at $V_{\mathrm{s}}$ = +500 mV and
$I_{\mathrm{s}}$ = 1.0 nA. Red (upper) and green (lower) lines represent the
spectra taken on sample # 1 at 22 K and sample # 2 at 4.2 K. The red spectrum
is shifted by 0.5 for clarity. The dashed line indicates the zero conductance
for the red (shifted) spectrum. The inset shows the spectrum with high energy
resolution.

However, the results obtained using these surface sensitive probes
occasionally do not reflect intrinsic bulk nature but reflect the nature
peculiar to the surface which is sometimes a stage of a novel phenomenon, when
the structure and electronic nature on the surface are different from those in
the bulk. Hence, it is necessary to uncover what type of surface structure and
electronic states are realized on an exposed surface, as a first step in
investigating the electronic nature of new compounds.

In this study, we performed STM and STS experiments on a cleaved surface of
NdO0.7F0.3BiS2 ($T_{\mathrm{c}}\sim$5.1 K), which is a member of the BiS2
superconductor family. A typical STM image on a cleaved surface shows several
features: (i) a square lattice with a period of $\sim$3.9 Å corresponding to
the in-plane lattice parameter, (ii) atomic defects, and (iii) streaked
depressions that are centered on each atomic defect. The tunneling
spectroscopy captures several unexpected phenomena. Its first feature is a
large spectroscopic gap ($\sim$40 mV) without a coherence peak, which survives
well above $T_{\mathrm{c}}$. It is considered that the observed gap is
inherent nature in the cleaved surface rather than in the bulk, since the gap
opening at approximately $E_{\mathrm{F}}$ is not consistent with the metallic
behavior in the bulk electric resistivity measurements. The second feature is
a square lattice characterized by an alternating arrangement of two types of
nanocluster. In one cluster, one-dimensional stripe electronic structures run
along one Bi-Bi direction, whereas, in the other cluster, the stripes run
along the other Bi-Bi direction. The third is a nanoscale electronic
inhomogeneity, which might have originated from the inhomogeneous
distributions of Bi defects and doped F atoms.

The single crystals used in this study were grown by a high-temperature flux
methodMNagao . The superconducting transition temperature of 5.1 K was
determined by magnetization and resistivity measurementsMNagao . The STM and
STS measurements were performed in a helium-gas environment at 4.2 and 22 K
using a laboratory-built STM. A surface on which the measurements were carried
out was prepared by cleaving the sample in situ. A bias voltage was applied to
the sample in all measurements. In this study, tunneling spectra were obtained
by numerically differentiating the $I$-$V$ characteristics measured at each
location.

Figure 2:  (Color online) (a) and (b) STM images on a 130 $\times$ 130 Å2
field of view (FOV) taken at $V_{\mathrm{s}}$ = +500 and -500 mV. (c)
Difference between (a) and (b) [$D(\boldmath{r})$-map];
$D(\boldmath{r})=Z(\boldmath{r},-500\ \mathrm{mV})-Z(\boldmath{r},+500\
\mathrm{mV})$. Red and blue boxes indicate the representatives of the
nanodomains where the stripe structures runs along $a_{x}$\- and
$a_{y}$-directions, respectively. Insets of (a), (b), and (c) are magnified
images in the FOV marked by black and white boxes in (a) to (c), respectively.
These magnified images are rotated by 40∘ in a clockwise fashion. Green
spheres represent Bi atom sites. (d) Fourier transform image
[$D(\boldmath{q})$] of (c). Red and blue dashed circles indicate the size of
$\Lambda$ (cutoff frequency) in the inverse FT analyses for the stripe
structures. The green dashed circle indicate the size of $\Lambda$ for an
inhomogeneous structure. (e) and (f) Magnified images of (d) at around
$\boldmath{q}_{\mathrm{x}}$ and $\boldmath{q}_{\mathrm{y}}$. Here, we increase
the contrasts in these magnified images for clarity. Dashed arrows in these
images indicate satellite peaks.

We show typical STM images in Figs. 1(a) and 1(b) indicating a square lattice
with a period of $\sim$3.9 Å corresponding to the in-plane lattice constant
($a_{0}$). This is confirmed from four spots in the FT image marked by red
circles in Fig. 1(c). In addition to the square lattice, several dark spots
can be observed. In the STM measurements of the layered compounds, it is quite
important to identify which plane appears as an exposed surface. In this
material, there are three possible atomic planes that could be exposed: (i)
NdO, (ii) S(2), and (iii) BiS(1). If the cleavage occurs between the NdO and
S(2) planes, as shown by a blue arrow in the inset of Fig. 1(a), two types of
atomic plane [NdO and S(2) planes] should be exposed. On the other hand, if
the cleavage occurs between two BiS(1) layers shown by a red arrow in the
inset, only one type of atomic plane [BiS(1) plane] should be exposed. Because
we obtained only one type of STM image, as shown in Fig. 1(a) and the
tunneling spectrum in Fig. 1(d) in this study, we conclude that the observed
surface is a BiS(1) plane. Recent calculations for the density of states
(DOS)BLi  show that the Bi-$p$ and S(1)-$p$ states predominantly contribute to
the DOS and that the Bi-$p$ DOS is higher than that of S(1)-$p$ near
$E_{\mathrm{F}}$. Therefore, the observed bright spots in the STM images are
considered to be Bi atoms.

Given that the observed bright spots are Bi atoms, the observed dark spots
pointed by the red arrow in Figs. 1(a) and 1(b) are Bi defects, since the
center of the dark spot coincides with one of the four Bi sites of the Bi
square lattice, as shown in Fig. 1(b). The density of the dark spots is about
3% per Bi atom, which is consistent with the results of the recent single-
crystal X-ray diffraction measurementsMiura . Besides the atomic defects,
slightly dark streaks run along approximately diagonal directions of the unit
cell. Representative examples are marked by two blue ellipsoids in Fig. 1(a).
The direction and length of the dark streaks somewhat vary. This variability
corresponds to the four tails extending from the center ($\boldmath{q}$ = 0)
of the FT image, as marked by yellow ellipsoids in Fig. 1(c). It appears that
the dark streaks are highly related to the atomic defects. Therefore, the dark
streak structures are believed to be the structural distortion relaxing the
mechanical stress due to atomic defects.

Figure 3:  (Color online) (a) and (b) Inverse FT images obtained by Fourier
filtering out all the modulations except those surrounding $\boldmath{q}_{x}$
(a) and $\boldmath{q}_{y}$ (b): Images of the real part of
$D(\boldmath{q}_{x},\boldmath{r})$ and $D(\boldmath{q}_{y},\boldmath{r})$, as
shown in Eq. (1). (c) Superposition of (a) and (b). Black dots and green
dashed lines correspond to the atomic defects and dark streaks on the surface,
respectively. Black boxes mark the dark streaks that coincide with the
boundary between two nanoclusters. (d) $O(\boldmath{r})$-map.
[$O(\boldmath{r})$ = $|D(\boldmath{q}_{x},\boldmath{r})|$ \-
$|D(\boldmath{q}_{y},\boldmath{r})|$]. Dashed and dotted circles indicate a
representative square lattice, which partially appears in (d). (e)
Autocorrelation image of (d).

Figure 1(d) shows typical tunnelling spectra at 4.2 and 22 K, which were
measured in different samples with different tips. Both spectra indicate (i) a
large energy asymmetry characterized by the higher conductance in positive
energy than in negative energy, and (ii) a spectroscopic gap characterized by
a depression of the spectral weight at approximately
$E_{\mathrm{F}}$Tunnel_spe . Surprisingly, the conductance is approximately
zero between $\pm$20 meV at both 4.2 and 22 K, as shown in the inset of Fig.
1(d). This means that there is no DOS at around $E_{\mathrm{F}}$. The observed
gap is not considered a superconducting gap, because it survives well above
$T_{\mathrm{c}}$ and does not have a clear coherence peak. These spectroscopic
features are inconsistent with the bulk properties showing a clear
superconducting transition and a metallic behavior of the resistivity just
above $T_{\mathrm{c}}$MNagao . Therefore, it is preferable to consider that
the observed spectroscopic features do not reflect the bulk property but
reflect the property unique to the surface.

To explore the spatial variation in the electronic structure, we compare two
STM images taken at $V_{\mathrm{s}}$ = +500 and -500 mV on the same FOV, as
shown in Figs. 2(a) [$Z$($\boldmath{r}$, +500 mV)] and 2(b)
[$Z$($\boldmath{r}$, -500 mV)], respectively. Apparently, there are two
features that are more pronounced in the image at $V_{\mathrm{s}}$ = -500 mV
than at +500 mV: (i) Fine stripe structures along the two $a$-axes and (ii)
inhomogeneous contrasts on the background. We take the difference between
these images [$D$($\boldmath{r}$) = $Z$($\boldmath{r}$, -500 mV) -
$Z$($\boldmath{r}$, +500 mV)], as shown in Fig. 2(c). This process cancels the
geometric information and extracts the electronic structures. In this case,
the $D(\boldmath{r})$-map indicates an energy asymmetry of the energy-
integrated LDOS from 0 to $\pm$ 500 meV. The two features in the
$Z$($\boldmath{r}$, -500 mV) map are emphasized in the $D(\boldmath{r})$-map.
Therefore, these two features are derived from the electronic spatial
variation. The FT image of the $D(\boldmath{r})$-map in Fig. 2(d) ensures the
existence of these two electronic features. The four spots marked by red and
blue dashed circles correspond to the fine stripe structures, whereas the
broad structure around $\boldmath{q}$ = 0 marked by a green dashed circle
corresponds to the inhomogeneous structure.

First, we focus on the fine stripe structures being elongated along one Bi-Bi
direction. As described above, the stripe structures can be classified into
two types. One modulates along the $a_{\mathrm{x}}$-direction marked by a blue
box in Fig. 2(c) ($x$-modulation), whereas the other modulates along the
$a_{\mathrm{y}}$-direction shown by a red box ($y$-modulation). These
modulations form two types of nanoscale cluster: In one cluster, the
$x$-modulation predominates, whereas, in the other, the $y$-modulation
predominates. The FT image of the $D(\boldmath{r})$-map corroborates the
presence of two modulations with a period of $a_{0}$, as shown in Fig. 2(d).
Here, we name the $\boldmath{q}$ vectors corresponding to these two
modulations as $q_{\mathrm{x}}$ and $q_{\mathrm{y}}$, respectively. Moreover,
it appears that the two types of cluster tend to be aligned alternatingly and
periodically in Fig. 2(c). In the FT image, in addition to $q_{\mathrm{x}}$
and $q_{\mathrm{y}}$, two satellite peaks can be seen at around
$q_{\mathrm{x}}$ and $q_{\mathrm{y}}$, as shown by dashed arrows in Figs. 2(e)
and 2(f). These satellites indicate that the amplitudes of the observed $x$\-
and $y$-modulations periodically and two-dimensionally vary in real space:
these satellites are indicative of the alternating arrangement of the observed
two types of cluster. The period of the amplitude modulations can be estimated
from $\delta\boldmath{q}$ = $\boldmath{q}_{\mathrm{x\ or\ y}}$ \-
$\boldmath{q}_{\mathrm{st}}$, where $\boldmath{q}_{\mathrm{st}}$ is the
position of the satellite peaks. The value of $\delta\boldmath{q}$ is
approximately 0.185$\times$2$\pi$/$a_{0}$
[0.245$\times$2$\pi$/($\sqrt{2}a_{0}$)]. This means that the period of the
amplitude modulation is approximately 5.4$a_{0}$ (4.1$\tilde{a}_{0}$,
$\tilde{a}_{0}$ is the length between Bi atoms along the diagonal direction of
the unit cell).

To visualize the corrugation of these clusters more clearly, we extract the
components associated with the $x$\- and $y$-modulations from the
$D(\boldmath{r})$-map using the inverse Fourier transformation as follows:

$\displaystyle
D(\boldmath{q}_{\mu},\boldmath{r})=\frac{2\pi}{N}\sum_{\boldmath{q}}D(\boldmath{q})\exp(-i\boldmath{q}\cdot\boldmath{r})$
$\displaystyle\exp\left[-(\boldmath{q}_{\mu}-\boldmath{q})^{2}/\Lambda^{2}\right],$
$\displaystyle\mu=x\ \mathrm{or}\ y,$ (1)

where $\Lambda$ is the cutoff wave number. Here, we set $\Lambda$ = 0.294
$\times$ 2$\pi$/$a_{0}$ (1/$\Lambda$ = 13.5 Å) corresponding to the red and
blue dashed circles in Fig. 2(d), as $\Lambda$ becomes longer than the
$|\delta\boldmath{q}|$. Figures 3(a) and 3(b) are the real parts of
$D(\boldmath{q}_{x},\boldmath{r})$ and $D(\boldmath{q}_{y},\boldmath{r})$,
respectively. A region with a large amplitude of the $x$-modulation shows a
small amplitude of the $y$-modulation and vice versa. This is also confirmed
more clearly in Fig. 3(c) in which Fig. 3(a) is superimposed on Fig. 3(b). We
further map out a quantity $O(\boldmath{r})$ =
$|D(\boldmath{q}_{x},\boldmath{r})|$ \- $|D(\boldmath{q}_{y},\boldmath{r})|$,
as shown in Fig. 3(d). [$|D(\boldmath{q}_{x},\boldmath{r})|$
($|D(\boldmath{q}_{y},\boldmath{r})|$) means the spatial variation in the
amplitude of the $x$-modulation ($y$-modulation)]. In this map, the nearly
4$\tilde{a}_{0}$ square lattice of the nanoclusters can be partially observed
as expected from the satellite peaks in the FT image of the
$D(\boldmath{r})$-map, as marked by white dashed circles in Fig. 3(d). Figure
3(e) shows the autocorrelation image of the $O(\boldmath{r})$-map. In this
image, the nearly 4$\tilde{a}_{0}$ square lattice is clearly observed. Thus,
our results suggest that the observed nanoclusters tend to form a
‘checkerboard’-like 4$\tilde{a}_{0}$ square lattice. The formation of the
lattice implies that some interactions exist between the nanoclusters.

Figure 3(c) shows the spatial correlation among the atomic defects, the dark
streak structures, and the observed nanoclusters. There is a weak correlation
between the atomic defects and the stripe structures in these nanoclusters.
The stripe structure tends to be suppressed around the atomic defects. The
positions of the dark streak structures sometimes coincide with the boundary
between two nanoclusters, as marked by the black boxes in Fig. 3(c). This
means that the dark streak structure tends to pin the boundaries of these
clusters. Thus, these local perturbations seem to distort the nearly
4$\tilde{a}_{0}$ square lattice.

The observed electronic features including a large spectroscopic gap and
‘checkerboard stripe’ electronic structure have not been anticipated in
previous investigations of the bulk properties. It is considered that the
observed spectroscopic gap seems to be inherent in the cleaved surface,
because of the inconsistency between the gap opening and the metallic behavior
in bulk transport measurements. If the observed checkerboard stripe structure
is related to the large spectroscopic gap, the checkerboard stripe structure
is the inherent phenomenon in the cleaved surface. However, it is also
possible to think that the checkerboard stripe coexists with the bulk
superconductivity, if it resides not only on the surface but also deep inside
the sample. Even though we cannot clarify whether the checkerboard stripe
exists only on the surface or in the bulk at present, our findings will be
crucial for understanding the electronic nature of this material, if the
checkerboard stripe coexists with the superconductivity.

In discussing the origin of the checkerboard stripe, it is important to
consider what is a driving force to generate the stripe structure which breaks
$C_{4}$-symmetry. One possible candidate is the softening of the phonons.
Recent calculations of the phonon spectra of LaO1-xFxBiS2 predicted that it is
possible for S(1) atoms to move towards Bi atoms along the $a$-axis (or
$b$-axis) owing to the unstable phonon at around $\Gamma$ under the proper
conditionsTYildirim . If this distortion occurs, the unit cell no longer
maintains the tetragonal symmetry ($C_{4}$-symmetry) and takes an orthogonal
symmetry instead. Such a broken symmetry of the crystal structure lifts the
degeneracy of the Bi6-$p_{x}$ and Bi6-$p_{y}$ bands, which seem to lie near
$E_{\mathrm{F}}$. This nonequivalent nature between the Bi6-$p_{x}$ and
Bi6-$p_{y}$ bands seems to induce the observed unidirectional electronic
structure (stripe structure). However, even if we adopt this idea, several
questions still remain. Why do the nanoclusters form the nearly
4$\tilde{a}_{0}$ square lattice? Is the condition of the exposed surface
obtained by cleaving the sample is appropriate for inducing such unstable
phonons? Thus, the origin of the observed ‘checkerboard stripe’ electronic
structure remains an open question.

Figure 4:  (Color online) (a) Low-pass-filtered image of Fig. 1(c). In this
low pass filtering, we set the cutoff frequency to be $|\boldmath{q}|$ = 0.58
$\times$ 2$\pi$/$a_{0}$ corresponding to the real-space cutoff radius of 6.7 Å
indicated by a black circle on the bottom-right corner. Red dots show the
positions of the atomic defects. (b) Tunneling spectra at several locations.
Red, green, and blue lines indicate the spectrum taken in the bright, medium
contrast, dark regions in (a).

Next, we focus on inhomogeneous structures. Figure 4(a) shows a low-pass-
filtered image of the $D$($\boldmath{r}$)-map, where the cutoff wave number is
$q_{\mathrm{cut}}$ = 0.58 $\times$ 2$\pi$/$a_{0}$ (corresponding to a cutoff
radius $r_{\mathrm{cut}}$ = 6.7 Å). This filtering subtracts the fine stripe
structures and extracts the electronic inhomogeneity. This filtered image
contains inhomogeneous spatial variations of the energy integrated LDOS in
both $Z$($\boldmath{r}$, -500 mV) and $Z$($\boldmath{r}$, +500 mV). In this
case, however, the contribution of $Z$($\boldmath{r}$, -500 mV) appears to be
larger than that of $Z$($\boldmath{r}$, +500 mV), because there is a larger
contrast regarding the inhomogeneous spatial variation in $Z$($\boldmath{r}$,
-500 mV) than in $Z$($\boldmath{r}$, +500 mV), as shown in Figs. 2(a) and
2(b). Thus, the bright region in the filtered $D$($\boldmath{r}$)-map seems to
correspond to the region with a higher DOS in negative energy. To further
explore how the shape of the tunneling spectrum changes along the observed
inhomogeneity, we take tunneling spectra at several locations with the
different intensities of $D$($\boldmath{r}$), as shown in Fig. 4(b). Here, we
set the set bias voltage $V_{\mathrm{s}}$ to be +500 mV, because the spatial
variation in the energy-integrated DOS is smaller in $Z$($\boldmath{r}$, +500
mV) than in $Z$($\boldmath{r}$, -500 mV). This set-up condition appears to
alleviate a set point effect on the tunneling spectrum. An apparent change in
the spectral weight lies below -100 meV. Thus, the LDOS below -100 meV is
closely related to the source of the inhomogeneity.

There are several possible sources of the electronic inhomogeneity. The first
candidate is the inhomogeneous distribution of the atomic defects. As seen in
Fig. 4(a), the defects prefer to sit in the dark region with the lower DOS in
negative energy. This slight correlation implies that the atomic defects are
related to the electronic inhomogeneity. These atomic defects would induce the
structural distortions around them. The distortions induced by the atomic
defects might provide a local modification of the hopping integrals, which
alters the electronic states locally. Another candidate is the inhomogeneous
distribution of the dopant F atoms. Usually, the dopant atoms distribute in a
random fashion. The random distribution of the dopant F atoms might provide
the inhomogeneous distribution of the carrier density, which also seems to
cause the electronic inhomogeneity.

In summary, we report on our STM and STS experiments on a cleaved surface of
NdO0.7F0.3BiS2 with $T_{\mathrm{c}}$ = 5.1 K. The STM images contain a square
lattice with a period of $\sim$3.9 Å corresponding to the lattice parameter
along the $a$-axis and the several atomic defects. The tunneling spectra
indicate a large spectroscopic gap ($\sim$40 mV), which is not the
superconducting gap. It is conceivable that the observed spectroscopic gap at
$E_{\mathrm{F}}$ is inherent in the cleaved surface, because the metallic
behavior in the bulk transport measurements is not consistent with the gap
opening. In addition to this spectroscopic gap, we find two unexpected
electronic structures: (i) ‘checkerboard stripe’ electronic structure and (ii)
a nanoscale electronic inhomogeneity. The former is characterized by an
alternating arrangement of two types of nanocluster. In one cluster, one-
dimensional stripe structures run along one of the crystal $a$-axes with a
period of $a_{0}$. In the other cluster, the stripes run along the other
$a$-axis. Furthermore, these clusters form a square lattice with a period of
nearly 4$\tilde{a}_{0}$ along the diagonal directions of the unit cell. The
latter seems to be related to the inhomogeneous distributions of the atomic
defects and of the dopant F atoms. Our results in this study will play an
important role in considering the origin of the superconductivity in this
system, if the observed electronic spatial structures coexist with the bulk
superconductivity.

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