Electronic correlations and spin frustration in the molecular conductors $κ$-(BEDT-TTF)$_2$X probed by magnetic quantum oscillations
Shamil Erkenov Sergej Fust Sebastian Oberbauer Werner Biberacher Natalia D. Kushch Harald Mueller Francis L. Pratt Rudolf Gross Mark V. Kartsovnik



details









Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
School of Natural Sciences, Technische Universität München, D-85748 Garching, Germany



Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
School of Natural Sciences, Technische Universität München, D-85748 Garching, Germany



Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
School of Natural Sciences, Technische Universität München, D-85748 Garching, Germany


Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany


Institute of Problems of Chemical Physics, Russian Academy of Sciences, Chernogolovka, 142432 Russian Federation


ESRF - The European Synchrotron, F-38043 Grenoble 9, France


ISIS Neutron and Muon Source, STFC Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, United Kingdom


Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany
School of Natural Sciences, Technische Universität München, D-85748 Garching, Germany
Munich Center for Quantum Science and Technology (MCQST), D-80799 Munich, Germany


mark.kartsovnik@wmi.badw.de
Walther-Meißner-Institut, Bayerische Akademie der Wissenschaften, D-85748 Garching, Germany



§ ABSTRACT 
The layered molecular conductors κ-(BEDT-TTF)_2X are a perfect experimental platform for studying the physics of the Mott transition and related exotic electronic states. In these materials, the subtle balance between various instabilities of the normal metallic state can be efficiently changed by applying a very moderate external pressure or by subtle chemical modifications, e.g. by a replacement of the insulating anion X^-, frequently referred to as “chemical pressure”. A crucially important but still unsettled issue is an exact understanding of the influence of physical and chemical pressure on the electronic structure. Here, we use magnetic quantum oscillations to explore in a broad pressure range the behavior of the key parameters governing the Mott physics, the electronic correlation strength ratio U/t and the spin frustration ratio t'/t in two κ salts, the ambient-pressure antiferromagnetic insulator with X = Cu[N(CN)_2]Cl and the ambient-pressure superconductor with X = Cu(NCS)_2.
Our analysis shows that pressure effectively changes not only the conduction bandwidth but also the degree of spin frustration, thus weakening both the electronic correlation strength and the magnetic ordering instability. At the same time, we find that the replacement of the anion Cu[N(CN)_2]Cl^- by Cu(NCS)_2^- results in a significant increase of the frustration parameter t'/t,  leaving the correlation strength essentially unchanged.


Electronic correlations and spin frustration in the molecular conductors κ-(BEDT-TTF)_2X probed by magnetic quantum oscillations
    M. V. Kartsovnik
    September 9, 2024
================================================================================================================================



§ INTRODUCTION

Layered organic charge-transfer salts have been extensively employed as model systems for exploring the correlation-driven Mott insulating instability and a plethora of associated fascinating phenomena ranging from conventional <cit.> and exotic <cit.> charge- and spin-ordered states, to quantum spin and electric-dipole liquids <cit.>, to valence-bond glass or solid <cit.> phases as well as unconventional superconductivity emerging in the direct proximity to an insulating ground state <cit.>.
Of particular interest is the family κ-(BEDT-TTF)_2X, where BEDT-TTF stands for the radical-cation bis(ethylenedithio)tetrathiafulvalene forming conducting layers alternating with insulating layers of a monovalent anion X^- <cit.>.
The organic molecules in the layers form an anisotropic triangular lattice of dimers with the on-site (intra-dimer) Coulomb repulsion significantly exceeding the nearest- and next-nearest-neighbor (inter-dimer) transfer integrals, U ≫ t,t', see refs. <cit.> for a review and inset in Fig. <ref>(a) below for illustration. This gives rise to a narrow, effectively half-filled conducting band.
Most of the abovementioned electronic states can be realized in these compounds, depending on subtle details of their crystal and electronic band structure, which can be controlled, e.g., by applying a moderate pressure, typically below 1 GPa, or by modifying the insulating anion.

Pressure is known to reduce the electronic correlation strength ratio U/t through increasing the conduction bandwidth, without changing the band filling. Therefore, the pressure-induced transition between the metallic and insulating ground states is generally referred to as a bandwidth-controlled metal-insulator transition (MIT).

The anion replacement in the κ salts has also been widely believed to primarily modify the bandwidth and therefore considered as “chemical pressure”, see, e.g.,
 <cit.>.
This interpretation has, however, been questioned by first-principles band structures calculations <cit.>, which suggested that the overall ground state properties of these materials are controlled by the degree of anisotropy of the dimer triangular lattice rather than by the correlation strength ratio U/t. The anisotropy of the triangular lattice, quantified by the ratio t'/t, is one of the key parameters in the physics of the Mott transition. Being directly relevant to the spin frustration, it is crucially important for the magnetic properties of the Mott-insulating state and for the nature of the eventual superconducting state in the adjacent domain of the phase diagram <cit.>. Through its impact on the magnetic ordering instability it should  also influence the critical electronic correlation strength required for the MIT, see, e.g., <cit.>.

The first experimental argument in support of the theoretical prediction <cit.> was obtained in the recent comparative study of magnetic quantum oscillations in two κ-(BEDT-TTF)_2X salts with X = Cu[N(CN)_2]Cl and Cu(NCS)_2 (hereafter referred to as κ-Cl and κ-NCS, respectively) under pressure <cit.>. These salts have very similar electronic band structures, but different ambient-pressure ground states <cit.>. κ-Cl is an archetypal antiferromagnetic Mott insulator, which transforms into a metal under a pressure of 20-40 MPa.  By contrast, the κ-NCS salt is already metallic at ambient pressure. Should the correlation strength be different in these salts, it must be reflected in the many-body renormalization of the effective mass <cit.>.

However, the recent experiment <cit.> has revealed no difference between the effective masses of the two salts in the pressure interval

40 ≲ p ≲ 100 MPa, corresponding to the close proximity to the MIT in κ-Cl, on the metallic side of its phase diagram. This result suggests that the mass renormalization, hence the correlation strength ratio U/t is approximately the same for both salts.
Given the virtually equal electronic correlation strength, the difference in the ambient-pressure ground states is natural to attribute to a difference in the spin frustration ratio t'/t. This would be fully consistent with the band structure calculations predicting a stronger frustration for the more metallic, though not weaker correlated, κ-NCS salt <cit.>. However, for a conclusive proof, it is important to provide an experimental test for the t'/t ratio in the two salts. Further, for a more accurate comparison of the many-body renormalization effects, an experimental data on the effective masses in a considerably broader pressure range is needed.

To this end, we have carried out a detailed study of magnetic quantum oscillations of interlayer magnetoresistance of the κ-Cl and κ-NCS salts in a broad range of pressures, up to p≈ 1.5 GPa. This range covers both the close neighborhood of the MIT in κ-Cl and the region deep in the normal metallic state, where the electronic correlations are significantly reduced. The data obtained allow us to evaluate both the electronic correlation strength and the degree of spin frustration and to trace their evolution with pressure. In this way, we have obtained a quantitative information on the influence of pressure and anion substitution on the Mott-insulating and magnetic-ordering instabilities in the two prominent members of the κ-(BEDT-TTF)_2X family.


The paper is organized as follows. The next section describes the experimental details and conditions. The experimental results and their discussion are given in Sec. <ref>. We start with the general behavior of the quantum oscillations of magnetoresistance (Shubnikov-de Haas, SdH oscillations) in the κ-Cl salt and its evolution with pressure.

In particular, we present here some details on the oscillation amplitude, possibly related to a pressure-dependent spin-splitting, and on the influence of the weak Fermi surface warping in the interlayer direction. For the κ-NCS salt, there is a vast literature on its high magnetic field properties, including quantum oscillations, see, e.g., refs. <cit.> for a review.

Therefore for this salt we only give a very brief account of the SdH oscillations in the Supplemental Material <cit.>, illustrating how the cyclotron masses were evaluated.

In Sect. <ref> we present detailed data on the pressure dependence of the SdH frequencies and analyze them in terms of the effective dimer model <cit.>. We show that both the anion replacement and the pressure lead to significant changes in the inplane anisotropy reflected, in particular, in the spin frustration ratio t'/t. In Sec. <ref>, the cyclotron effective masses corresponding to the two fundamental SdH frequencies are presented for both salts and compared with each other. Throughout the entire pressure range studied, both salts show very similar mass values. Moreover, the overall mass behavior is remarkably well described by the Brinkman-Rice model, indicating the electron-electron interactions as a dominant mechanism of the pressure-dependent mass renormalization and allowing its quantitative analysis.

Our conclusions are summarized in Sec. <ref>.




§ EXPERIMENTAL

The single crystals used in the experiment were grown electrochemically. The κ-Cl crystals were grown following the procedure described in literature <cit.>, using the carefully purified commercial BEDT-TTF donor. For the κ-NCS crystals, the BEDT-TTF donor was synthesized according to the specially developed protocol <cit.> using [1,3]-dithiolo-[4,5-d][1,3-dithiole]-2,5-dione (thiapendione, TPD) as a starting compound. This procedure yielded crystals of very high quality (see the the Supplemental Material <cit.>), which was particularly important for the observation and quantitative analysis of the high-frequency (F_β) SdH oscillations.

For the measurements, two

crystals of each salt, κ-Cl and κ-NCS, have been selected.
SdH oscillations were studied in the interlayer transport geometry, that is conventional for the layered organics <cit.>. The resistance across the layers was measured using the standard four-probe low-frequency (f ∼ 10 - 300 Hz) a.c. technique. Annealed 20 μm-thick platinum wires, serving as current and voltage leads, were attached to the samples with a conducting graphite paste yielding the contact resistance ∼ 10-30 Ω at low temperatures.
The samples were mounted in a Be-Cu clamp pressure cell and cooled down in ^3He or ^4He variable-temperature inserts placed into a 15 T superconducting solenoid.
The pressure p was evaluated at room temperature and at 15 K using a calibrated n-doped InSb pressure gauge (see the Supplemental Material to ref. <cit.> for details). In the high-pressure range, above 0.8 GPa, the calibration was crosschecked using the p-linear resistance of a manganin wire <cit.> as a reference. In what follows, all the indicated pressure values are those determined at T =15 K. The error in the pressure determination did not exceed 10 MPa at p < 0.2 GPa and 5% at higher pressures.

All the measurements on κ-Cl sample #1 and on both κ-NCS samples were done in a magnetic field applied perpendicular to the plane of conducting layers (crystallographic ac-plane and bc-plane for κ-Cl and κ-NCS, respectively). This is a conventional geometry for probing the inplane charge dynamics in layered materials as the field induces cyclotron orbits in the layer plane. The κ-Cl sample #2 was used partly in the same geometry at lower pressures, p < 0.4 GPa, whereas for the rest of the measurements this sample was tilted by an angle of θ = 25^∘ from the perpendicular field direction, as explained in Sec. <ref>. Taking into account the quasi-2D character of the present materials, we simply multiply the SdH frequencies and cyclotron masses, determined in the tilted fields, by the factor cosθ to obtain the values corresponding to the perpendicular field.





§ RESULTS AND DISCUSSION
 


 §.§ SdH oscillations in κ-Cl: general features
 






Figure <ref> shows examples of the SdH oscillations recorded for κ-Cl sample #1 at different pressures, at the base temperature of the ^3He cryostat.


For each pressure the oscillating signal is normalized by the respective field-dependent nonoscillating background R_bg obtained by a low-order polynomial fit of the as-measured resistance R(B): R_osc/R_bg≡[ R(B) - R_bg(B) ]/R_bg(B). In full agreement with the previous reports <cit.>,
two fundamental frequencies are observed, revealing the Fermi surface topology typical of the κ salts <cit.>, see also Fig. <ref>(b) below. The lower frequency, F_α, is associated with the classical orbit on the Fermi pocket centered at the Brillouin zone boundary and varies between ≈ 530 and 675 T upon increasing pressure from 75 MPa to 1.5 GPa. The dominant oscillations clearly resolved at all pressures have a higher frequency, F_β∼ 4 kT, corresponding to a cyclotron orbit area equal to that of the first Brillouin zone. This orbit is caused by magnetic breakdown between the α pocket and a pair of open sheets and thus represents the entire Fermi surface (in the two-dimensional, 2D, representation, i.e., the Fermi surface in the plane of the conducting molecular layers)  <cit.>.



The β oscillations exhibit pronounced beating, indicating that there are in fact two frequencies close to each other.
This frequency splitting, Δ F_β/F_β∼ 0.01, most likely originates from the maximal and minimal cross-sections of the three-dimensional (3D) Fermi surface cylinder slightly warped in the interlayer direction (see the Supplemental Material of ref. <cit.>), a phenomenon observed earlier on a number of organic <cit.> and inorganic <cit.> layered materials.
For example, at p = 0.3 GPa we find two beat nodes, at 9.50 T and at 12.21 T, respectively. From this we roughly evaluate the warping of the Fermi surface: Δ k_F/k_F≃Δ F_β/2F_β≈ 0.55 × 10^-2 (here we used the experimental value F_β(0.3GPa)= 3900 T) <cit.>. This warping is similar to that in the isostructural ambient-pressure superconductor κ-(BEDT-TTF)_2Cu[N(CN)_2]Br <cit.> and an order of magnitude stronger than in the sibling κ-NCS salt <cit.>.

At increasing pressure up to 1.36 GPa, the beat nodes shift to higher field, indicating an increase of the beat frequency, hence of the Fermi surface warping by ≃ 25%.
A noticeable pressure-induced enhancement of the interlayer coupling is common for the layered organic conductors with their relatively soft crystal lattices.
Interestingly, however, the node positions start to shift down upon further pressurizing beyond 1.4 GPa.
This apparent weakening of the interlayer coupling at high pressures is unusual and may deserve further attention.

One can see that the amplitude of the oscillations in Fig. <ref> varies in a nonmonotonic manner at changing pressure. In Fig. <ref> we plot the p-dependence of the amplitudes of main peaks in the fast Fourier transform (FFT) spectra of the oscillatory magnetoresistance, in the field window  12 T to 15 T.

The amplitude of the β oscillations, see Fig. <ref>(a), exhibits pronounced minima at p ≃ 0.2 GPa and 0.9 GPa. Simultaneously, the amplitude ratio between the second and first harmonics, A_2β/F_β, shown in Fig. <ref>(b), displays sharp peaks at the same pressures. This behavior is strongly suggestive of the spin-zero effect caused by the periodic modulation of the oscillation amplitude by the spin-splitting factor R_s^(r) = cos(rπ/2m_c/m_0g), where r is the harmonic index, g is the Landé g-factor averaged over the cyclotron orbit, and m_0 the free electron mass <cit.>. For the quasi-2D organics, this effect has been widely known <cit.> as a periodic vanishing of the fundamental harmonic amplitude (with a simultaneously peaking second harmonic) when rotating the magnetic field, due to the angle-dependent cyclotron mass m_c(θ) = m_c(0)/cosθ. Knowing the effective cyclotron mass, such angle-dependent data can give useful information about the many-body renormalization of the g-factor. It would be interesting to carry out similar measurements on the κ-Cl salt at different pressures. This should provide data for a comparison between the p-dependent renormalization effects on the g-factor and on the effective mass.

The variation of the α-oscillation amplitude with pressure is shown in Fig. <ref>(c). Here we do not see spin-zero dips. A likely reason for that is a significantly lower cyclotron mass, m_c,α≈ m_c,β/2 (see Sect. <ref>), which enters the argument of cosine in the expression for R_s and thus leads to its weaker variation under pressure. It is possible that the nonmonotonic behavior with a maximum near p=0.5 GPa is caused by the spin-splitting factor slowly changing with pressure. On the other hand, we note that the A_α(p) dependence resembles that of A_β(p) in Fig. <ref>(a) once we ignore the modulation of the latter by the oscillating spin-splitting factor. In both cases the amplitudes display a global maximum near 0.5 GPa and a general trend to decrease at high pressures. The mechanisms behind this behavior may be common for the α and β oscillations. For example, one can speculate that the initial increase of the amplitude at low pressures is related to the rapid decrease of both cyclotron masses and concomitant weakening of temperature and scattering damping effects on the quantum oscillations <cit.>. The following slow decrease of the amplitude above 0.5 GPa may come from a pressure-induced enhancement of the Fermi surface warping (i.e. enhancement of the interlayer coupling), which should lead to a decrease of the number of charge carriers contributing in phase to the quantum oscillations.


The beating of the β oscillations and the resulting splitting of the FFT peak obviously affects the precision of determination of the mean Fermi surface area, which we will need in the following for evaluation of the frustration parameter t'/t.
This source of error can be avoided by aligning the sample in the direction corresponding to a maximum in the classical angle-dependent magnetoresistance oscillations (AMRO) <cit.>. At such directions, known also as Yamaji angles, all cyclotron orbits on a weakly warped cylindrical Fermi surface have the same area <cit.>, hence, contribute in phase to the quantum oscillations. As a result, when the sample is turned in a magnetic field, approaching a Yamaji angle, the beat frequency vanishes and the SdH amplitude acquires a local maximum.
This effect is illustrated in Fig. <ref>, where the field-dependent resistance of two samples mounted side by side in the pressure cell but aligned differently with respect to the magnetic field is plotted. Here, panel (a) shows sample #1 aligned with its conducting layers perpendicular to the field. Sample # 2 in Fig. <ref>(b) is tilted from the perpendicular orientation by angle θ≈ 25^∘, which is close to the first Yamaji angle for the β orbit <cit.>. As a result, the amplitude of the β oscillations is strongly enhanced and no trace of beating is seen. The fast Fourier transforms (FFT) of both oscillating signals are shown in  Fig.  <ref>(c). Here, in order to facilitate a direct comparison between different orientations, we multiply the frequencies by cosθ, thereby reducing them to the values corresponding to θ = 0^∘.

One readily sees that the F_β peak for sample #2 (red curve) is greatly enhanced and, in contrast to sample #1 (black curve), shows no splitting.

Thus, at θ≈ 25^∘  we significantly gain in the accuracy of both the frequency and amplitude of the β oscillations. Therefore, most of the measurements on sample #2 was done at this orientation. Note, however, that at this orientation the information on the Fermi surface warping is lost and the α oscillations are significantly suppressed, in comparison with those in the perpendicular field. Hence, a part of the measurements on sample #2 and all studies of sample #1 were done at θ = 0^∘.
In what follows, we will present the SdH frequencies and effective masses obtained for κ-Cl in both the perpendicular and the tilted orientations.






We also note that due to the very high electronic anisotropy of the κ-NCS salt (see the Supplemental Material <cit.> and references therein) the abovementioned effect of AMRO on the SdH oscillations is absent in this material. Therefore, all measurements on κ-NCS have been done in the perpendicular field geometry.




 §.§ p-dependent SdH frequencies and inplane anisotropy
 
In this section we present a detailed analysis of the SdH frequencies, which are fundamentally determined by the area of the relevant Fermi surface cross-section S_i through the Onsager relation <cit.>, F_i = ħ e/2πS_i, with ħ being the Planck constant and e the elementary charge.
Figure <ref>(a) shows the pressure-dependent frequencies of the β oscillations in κ-Cl sample #2 (red symbols)  and κ-NCS (blue symbols).

For κ-Cl, the empty circles correspond to the perpendicular field geometry and the filled circles are the data taken at θ = 25^∘  and multiplied by cosθ. Sample #1 was measured simultaneously with #2, but at θ = 0^∘ and showed consistent values within the error bars. For κ-NCS, the filled circles are the averaged values obtained on two samples  measured simultaneously; the difference between the samples lies within the indicated error bars.
The stars are the data obtained in our previous dilution-fridge experiment on κ-Cl and κ-NCS at pressures up to 0.1 GPa <cit.>.

 

 As already mentioned, the β oscillations are associated with the magnetic-breakdown orbit with the area equal to the Brillouin zone area.
 
 Indeed, the zero pressure values, F_β^Cl(0) = (3836 ± 5) T and F_β^NCS(0) = (3867 ± 7) T yield the areas (36.62± 0.05) nm^-2 and (36.91± 0.05) nm^-2, respectively,
perfectly coinciding with the low-temperature Brillouin zone areas of these salts <cit.>.






The shapes of the p dependence in Fig. <ref>(a) look slightly different from each other. However, by plotting the relative change of the frequency under pressure, see Fig. <ref>(b), we find that the difference between the two salts does not exceed the experimental error bars. Moreover, our data are consistent with the quasi-linear p dependence of the Brillouin zone areas [triangles in Fig. <ref>(b)] based on the X-ray data <cit.>. We note that the X-ray studies  <cit.> have been done at room temperature. However, their good agreement with our low-temperature SdH data suggests that the compressibility does not change significantly upon cooling.



Plotted in Fig. <ref>(c) is the pressure dependence of the α frequency. For κ-NCS the symbol and color codes are the same as in Fig. <ref>(a). For κ-Cl, the data (circles) have been taken on sample #1 in the perpendicular field geometry. For pressures below 0.1 GPa, the results from our previous dilution fridge experiment <cit.> are added (stars). Both data sets are perfectly consistent with each other. Therefore, we will not distinguish between them in the following.

For κ-NCS our data set is consistent with the early study by Caulfield et al. <cit.>. As was already noticed by those authors, the relative increase of F_α with pressure is much stronger than that of F_β. The κ-Cl salt shows the same, even more pronounced trend.
At lower pressures, p < 0.3 GPa, the α frequency increases at a relative rate of  ≃ 0.25 GPa^-1 for κ-NCS and ≃ 0.4 GPa^-1 for κ-Cl [cf. the relative increase rate of the β frequencies in Fig. <ref>(b) is only ≈ 0.04 GPa^-1].
Interestingly, for κ-Cl, the absolute changes of F_α(p) and F_β(p) are virtually the same in this pressure range, see the inset in Fig. <ref>(c). This suggests that, in contrast to the rapidly expanding α pocket, the rest of the Fermi surface remains almost unchanged. At higher pressures, the increase of F_α becomes more moderate, with a slope saturating at ∼ 0.15 GPa^-1.

For κ-NCS, due to the weakness of the β oscillations at p< 0.3 GPa,

a sufficiently accurate comparison of Δ F_α(p) and Δ F_β(p) is difficult. However, qualitatively, the behavior is similar to that of κ-Cl.



The difference in the behaviors of the α and β frequencies is summarized as the p-dependent ratio F_α/F_β in Fig. <ref>(d).
Let us discuss this ratio in terms of the electronic anisotropy of the conducting layers, in other words, in terms of the shape of the 2D Fermi surface.

 
To this end, we follow the approach <cit.> based on the effective dimer model commongly used for the κ salts. This is a tight-binding model of an anisotropic triangular lattice of BEDT-TTF dimers with the nearest and next-nearest transfer integrals, t and t^', respectively [see inset in Fig. <ref>(a)], and the dispersion relation:








    ϵ(𝐤) = 4tcos( k_x x/2) cos( k_y y/2) +2t^'cos( k_y y ).

Here, x and y should be substituted by the crystallographic parameters a(c) and c(b) in κ-Cl(-NCS), respectively.
The above equation is a parametric expression for the Fermi surface which directly determines the ratio  between the Fermi surface areas S_α and S_β, hence the ratio F_α/F_β through t^'/t, the spin frustration parameter of the anisotropic triangular lattice of the molecular dimers <cit.>.

Fitting the experimental data in Fig.<ref>(d) with Eq. (<ref>), we evaluate the frustration ratio t^'/t  and its dependence on pressure for both salts, as shown in Fig. <ref>(a).
The first, obvious result is that the frustration in the metallic κ-NCS salt  is significantly stronger than in the ambient-pressure Mott insulator κ-Cl. While this difference was predicted by some band structure calculations <cit.>, our data provide, to the best of our knowledge, the first direct experimental evidence for that.

Another important observation is that even our quasi-hydrostatic pressure significantly changes the electronic anisotropy in the conducting layers, leading to an enhancement of the spin frustration.
In a broad pressure range the t^'/t ratio increases with an approximately constant rate of ≃ 0.07 GPa^-1, which even increases below 0.3 GPa, as the system approaches the MIT. The overall increase of the frustration ratio in the studied pressure range is ≳ 20%. In particular, at 1 GPa the frustration in the κ-Cl salt already exceeds the ambient-pressure value for κ-NCS.


Thus, besides the well-known effect of pressure on electronic correlation strength, it is important to take into account its strong influence on magnetic ordering instability in these materials.

In Fig. <ref>(b) we show the Fermi surfaces of κ-Cl and κ-NCS, calculated using Eq. (<ref>) and the experimental SdH frequencies, for the lowest and for the highest pressure. Even though the crystal lattice compressibility is assumed to be isotropic in the layers plane, as it is at room temperature <cit.>, the changes in the Fermi surfaces of both salts are obviously anisotropic. While the α pocket shows a significant increase along its short axis (k_x), the rest of the Fermi surface remains almost the same. Such a behavior is indeed observed experimentally on κ-Cl at pressures of up to 0.3 GPa, as noted above. At higher pressures, however, the absolute changes Δ F_β(p) and Δ F_α(p) deviate from each other, see, e.g., the inset in Fig. <ref>(c). This means that the Fermi surface also expands in the k_y direction. The apparent absence of such expansion in Fig. <ref>(b) is most likely due to a limited precision of the simple effective dimer model employed here. It would be highly interesting to perform a more elaborated analysis confronting our data with an ab-initio band structure calculation taking into account electronic correlations. This, however, appears to be a very challenging task, requiring, furthermore, detailed low-T structural data at high pressures. On the other hand, our main conclusions concerning the comparison of the spin frustration in the present two compounds and their pressure dependence seem to be  robust against small quantitative corrections.







 §.§ Effective cyclotron masses
 
The effective cyclotron masses were evaluated from the T-dependence of the amplitude A_i(T) of the fundamental harmonic of the SdH oscillations in a conventional way based on the Lifshitz-Kosevich (LK) theory <cit.>.



Details of the evaluation including some examples are given in the Supplemental Material <cit.>.




The results for the mass (in units of the free electron mass m_0) on the β orbit, characterizing the entire Fermi surface, are plotted in Fig. <ref>. Here the blue  symbols represent κ-Cl sample #2. The filled circles and diamonds correspond to the data obtained at θ = 0^∘ (field perpendicular to the layers) and at 25^∘ (near the AMRO peak), respectively. The latter are multiplied by cos 25^∘.

Sample #1, measured simultaneously with sample #2, yielded very similar mass values (not shown in Fig. <ref>, for the sake of clarity). The empty circles are the data obtained on sample #1 in our earlier lower-pressure experiment <cit.>.
The green symbols show the mass for the κ-NCS salt obtained in this work (filled triangles) and in Ref. <cit.> (empty triangles).
Due to a larger magnetic breakdown gap, the β oscillations in κ-NCS are relatively weak (see the Supplemetal Material <cit.>), which leads to a larger error bar and stronger scattering of the data.


Within the experimental error, the κ-Cl and κ-NCS salts exhibit the same behavior. The initial rapid decrease of the mass occurring as

we are moving away from the MIT slows down with increasing pressure and saturates above 1 GPa at the level m_c,β≃ 2.5 m_0. Note that this value is close to the band cyclotron mass m_c,β,band = 2.6m_0 <cit.> calculated for κ-NCS from the band structure neglecting many-body interactions. Thus, it appears that at pressures above 1 GPa we have essentially a noninteracting electron system. Taking into account that the only significant change in our materials within the rather narrow range 0 < p < 1 GPa is the electronically driven MIT, it is natural to attribute the effective mass renormalization entirely to electronic correlations.


Other renormalization effects, such as due to electron-phonon interactions, not directly linked to the MIT, are not expected to change notably within this pressure range and, therefore, are most likely insignificant.

The above argument justifies the analysis of the pressure-dependent effective mass in terms of the electronic correlation strength ratio U/t. In particular, the fact that the masses m_c,β in κ-Cl and κ-NCS are very similar at all pressures and approach the same high-p limit m_c,β,band further substantiates the earlier conclusion <cit.>, inferred from lower-pressure data, that the correlation strength is indeed essentially the same in both salts.



Turning to a more quantitative analysis, the previous, low-pressure experiment <cit.> has revealed a simple inverse-linear p-dependence of the mass, which was interpreted in terms of a Brinkman-Rice-like (BR-like) renormalization <cit.>. The present data, obtained in a broader pressure range, reveal a deviation from this behavior starting from at p ≃ 0.25 GPa.

This is clearly seen in the inset in Fig. <ref>, where the inverse mass of κ-Cl is plotted and the dashed straight line is the linear fit to the low-pressure data <cit.>. It should be noted that the linear dependence, m_c^-1∝ (p-p_0), was inferred from the BR theory <cit.>, assuming a linear pressure dependence of the correlation strength ratio. This approximation works well in a narrow pressure interval near the MIT, where the change of the ratio U/t does not exceed 1-2% <cit.>.
However, for a broader range one should take into account that the inter-site transfer integral t is significantly more sensitive to pressure than the on-site (intra-dimer) Coulomb repulsion U <cit.>.
In this case, a more reasonable approximation is <cit.> to assume U = const and expand t rather than U/t linearly in pressure:


    t(p) ≈ t_0[1 + γ(p-p_0)],

where p_0 is the critical pressure where the mass diverges in the BR model, t_0 ≡ t(p_0) and γ is a proportionality factor. Further following  <cit.>, we set the critical on-site repulsion U_0 proportional to the conducting bandwidth, hence to t(p). Then, the BR renormalization of the effective mass <cit.>, m_c =  m_c,band/[1 - (U/U_0)^2  ], can be as:

    m_c =
     m_c,band[1-1/[1+γ(p-p_0)]^2]^-1 .

Here, we replaced the usual quasiparticle effective mass m^∗ and band mass m_band considered in the original BR theory <cit.> by the respective cyclotron masses considered in the LK theory of magnetic quantum oscillations, since the many-body renormalization effects are the same in both cases <cit.>.

Despite its rather simple form,  Eq. (<ref>) fits the experimental data remarkably well throughout the whole pressure range. This is shown by the red dashed line in Fig. <ref> fitting the κ-Cl data <cit.>.


We, therefore, assume that it provides a realistic estimate of the parameters characterizing the electronic system: m_c,β,band = (2.07 ± 0.1)m_0, p_0 = (-0.28 ± 0.04) GPa, and γ = (0.77 ± 0.11) GPa^-1. The fit to the κ-NCS dataset yields very similar parameters, although with considerably larger error bars, see the Supplemental Material <cit.>. The evaluated band mass is somewhat smaller than the abovementioned calculated value, 2.6m_0 <cit.>, but the difference does not exceed the uncertainty of the band structure calculations <cit.>. The BR critical pressure is comparable to that obtained from an even simpler  low-p fit <cit.> shown by the dashed straight line in the inset in Fig. <ref>. Finally, within the present approach, the sensitivity of the electronic correlation strength to pressure is basically determined by the coefficient γ = dt/t_0/dp.

The obtained value is an order of magnitude higher than that inferred from the band-structure calculations <cit.>. The calculations yielded the U/t ratio in κ-NCS decreasing by only 5% upon increasing pressure from 0 to 0.75 GPa, which would imply γ≈ 0.07 GPa^-1. A similarly strong disagreement with the theoretical predictions has already been detected in the experimental data taken in a narrow pressure interval very close to the MIT <cit.>. Now it is confirmed to exist over a much broader range where the effective mass is no longer inversely-linear in p and even approaches the noninteracting band mass value.







Thus far, we have considered the cyclotron mass on the magnetic-breakdown β orbit encircling the entire 2D Fermi surface. It is interesting to compare it with the mass on the classical orbit α, which involves only one-half of the charge carriers. In this way we may obtain information on the momentum dependence of the electronic interactions. For example, in another organic salt, κ-(BETS)_2Mn[N(CN)_2]_3, displaying the MIT, the mass renormalization on the α orbit was found to be enhanced in comparison to the rest of the Fermi surface in close proximity to the transition <cit.>. Figure <ref> summarizes our  results on m_c,α(p) in κ-Cl and κ-NCS. All the data in the figure have been taken in the perpendicular field configuration, as at the tilted field the α oscillations in κ-Cl were too weak (see Fig. <ref>) for an accurate mass determination.


For κ-Cl, the α mass is almost exactly one-half of the β mass and this relation is virtually independent of pressure. To illustrate this, we plot the ratio m_c,β/m_c,α in the inset in Fig. <ref>. A linear fit to the data (dashed line in the inset), has a very slight slope, (-0.055 ± 0.04) GPa^-1, lying within the error bar. Such a weak variation, even if it reflects a real trend, may be attributed to a weak pressure dependence of the band masses.



The blue dashed line in the main panel of Fig. <ref> is the BR fit according to Eq. (<ref>). It yields the parameters: m_c,α,band = (1.05 ± 0.07)m_0, p_0 = (-0.29 ± 0.04) GPa, and γ = (0.81 ± 0.16) GPa^-1.

As expected, the band mass is approximately one-half of the β band mass obtained above. The other two parameters are very close to those obtained for the β orbit. All in all, we observe no evidence of a difference in the mass renormalization on the α and β orbits. Thus, within the accuracy of our experiment the electronic correlations appear to be  momentum-independent in the κ-Cl salt, in contrast to those in κ-(BETS)_2Mn[N(CN)_2]_3.


For the κ-NCS salt (green triangles in Fig. <ref>), the α-mass values lie slightly higher than for κ-Cl <cit.>. The difference is likely caused by a larger, than in κ-Cl, size of the α orbit (see Sec. <ref>), hence a higher band cyclotron mass. Indeed, the fit with Eq. (<ref>) gives m_c,α,band = (1.18 ± 0.06)m_0, that is 10% higher than in the κ-Cl salt.




As to the other fitting parameters, the sensitivity to pressure, γ = (0.78 ± 0.13) GPa^-1 is almost the same as for κ-Cl, whereas the  BR critical pressure p_0 = (-0.33 ± 0.03) GPa is slightly lower.

It is also lower than the value, p_0 ≃ -0.29 GPa, obtained from the fit to the m_c,β(p) dependence in the same salt, see Fig. S4 in the Supplemental Material <cit.>.
The relatively low p_0 value for the α orbit might be a sign of weaker electronic correlations. If so, this would imply that the correlation effects are different on different parts of the Fermi surface in κ-NCS, weaker on the α pocket and stronger on the open sheets. However, we should keep in mind that the mentioned differences in p_0 are small and comparable to the evaluation error bars. Here, the limiting factor is the rather large error bars in the m_c,β(p) dependence caused by the low amplitude of the magnetic-breakdown β oscillations in κ-NCS. For making a definitive conclusion, further measurements at higher magnetic fields, B>30 T, would be very helpful. While high-field quantum oscillations experiments have been done on κ-NCS at ambient pressure, see, e.g., refs. <cit.>, we are unaware of similar measurements under pressure.










§ CONCLUSIONS

Using the SdH oscillation technique, we have been able to trace the evolution of the electronic correlation strength as well as the spin frustration ratio in the κ-(BEDT-TTF)_2X salts with X = Cu[N(CN)_2]Cl and Cu(NCS)_2 in a broad pressure range up to 1.5 GPa corresponding to an almost two-fold change of the conduction bandwidth, according to our estimations.



From the systematic analysis of the SdH amplitude, we have determined the renormalized

effective cyclotron masses. The renormalization is found to be the same for the α and β orbits. This suggests that electronic correlations are homogeneous over the Fermi surface.

Throughout the entire pressure range studied the behavior of the effective cyclotron mass is remarkably well described by the BR model under the assumption of a linear-in-pressure transfer integral t(p) and a p-independent on-site Coulomb repulsion. This approximation was recently shown to work well for the inorganic 3D Mott insulator NiS_2 at pressures between 3 and 11 GPa <cit.> and also seems to be very reasonable in our case. The sensitivity of the transfer integral to pressure, γ = dt/t_0/dp≃ 0.8 GPa^-1, was estimated by fitting the experimental data with the model Eq. (<ref>). This result is consistent with the previous estimations based on low-pressure data <cit.>, but is an order of magnitude higher than inferred from the band structure calculations <cit.>. This stark discrepancy challenges our understanding of the correlation effects on the band structure near the bandwidth-controlled MIT.


Our data confirm and further extend to a broad pressure range the earlier finding <cit.> that the correlation strength is the same in the ambient-pressure insulator κ-Cl and in the superconducting κ-NCS. By contrast, the spin frustration turns out to differ considerably in the two salts. To estimate the frustration ratio t^'/t, we use the fact that this parameter is intimately connected with the shape of the Fermi surface and thus can be extracted from the relationship of the SdH frequencies F_α and F_β. To this end we followed the approach based on the effective dimer model <cit.>. The resulting ambient-pressure values are t^'/t ≈ 0.57 and 0.69 for κ-Cl and κ-NCS, respectively. Both values are somewhat higher than those obtained in first-principles band structure calculations <cit.>. It would be highly interesting to revise the calculations, taking into account our results on the SdH frequencies. At the same time, in line with the theoretical predictions, for the κ-NCS salt the t^'/t ratio is significantly higher than for κ-Cl. This result clearly demonstrates the dominant role of the spin frustration in the “chemical pressure” effect within, at least, the present pair of κ salts with different anions. It is interesting to perform a similar study on other κ salts, in particular, on the metallic salt with X = Cu[N(CN)_2]Br isostructural to κ-Cl and on the spin-liquid candidate with X = Cu_2(CN)_3.

Finally, our analysis of the SdH frequencies  clearly reveals a considerable pressure effect on the spin frustration. For both salts, the t^'/t ratio increases by ≳ 20% within the studied pressure range. Thus, one has to take into account the influence of pressure on both the electronic correlations and the magnetic ordering instability when studying the electronic phase diagram of our materials and, possibly, of the other κ salts.



We are thankful to K. Kanoda, P. Reiss, and V. Zverev for stimulating and illuminating discussions. The work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) via Grants No. KA 1652/5-1 and No. GR 1132/19-1.











101
fxundefined [1]
 ifx#1

fnum [1]
 #1firstoftwo
 secondoftwo
 
fx [1]
 #1firstoftwo
 secondoftwo
 





noop [0]secondoftwo

ref[1]@startlink#1@href
href[1]#1@endlink
anitize@url [0]`
12`$12`&12`#12`1̂2`_12`%12
startlink[1]
endlink[0]

rl [1]href #1












@bib@innerbibempty

[Kanoda(1997)]kano97
  author author K. Kanoda, title title Recent progress in NMR
  studies on organic conductors, @noop  journal
  journal Hyperfine Interact. volume
  104, pages 235 (year 1997)NoStop
[Miyagawa et al.(2004)Miyagawa, Kanoda, and Kawamoto]kano04
  author author K. Miyagawa, author K. Kanoda,  and author A. Kawamoto,  title title NMR studies on two-dimensional
  molecular conductors and superconductors: Mott transition in
  κ-(BEDT-TTF)_2X, https://doi.org/10.1021/cr0306541
  journal journal Chem. Rev. volume 104, pages 5635 (year
  2004)NoStop
[Powell and McKenzie(2006)]powe06
  author author B. J. Powell and author R. H. McKenzie, title title Strong electronic
  correlations in superconducting organic charge transfer salts, https://doi.org/10.1088/0953-8984/18/45/R03 journal journal J. Phys.: Condens. Matter volume 18,  pages R827 (year 2006)NoStop
[Seo et al.(2004)Seo,
  Hotta, and Fukuyama]seo04
  author author H. Seo, author C. Hotta, and  author H. Fukuyama, title title Toward systematic understanding of diversity of
  electronic properties in low-dimensional molecular solids, @noop 
  journal journal Chem. Rev. volume 104, pages 5005 (year
  2004)NoStop
[Mori(2016)]mori16
  author author T. Mori, title title Non-stripe charge order in
  dimerized organic conductors, https://doi.org/10.1103/PhysRevB.93.245104 journal journal Phys. Rev. B volume 93, pages 245104 (year 2016)NoStop
[Oshima et al.(2017)Oshima,
  Cui, and Kato]oshi17
  author author Y. Oshima, author H.-B. Cui,  and author R. Kato, title title Antiferromagnetic insulating ground state of
  molecular π-d system λ-(BETS)_2FeCl_4 (BETS =
  bis(ethylenedithio)tetraselenafulvalene): A theoretical and experimental
  review, https://doi.org/10.3390/magnetochemistry3010010 journal journal Magnetochemistry volume 3, pages 10 (year 2017)NoStop
[Okazaki et al.(2013)Okazaki, Ikemoto, Moriwaki, Shikama, Takahashi, Mori, Nakaya, Sasaki, Yasui, and Terasaki]okaz13
  author author R. Okazaki, author Y. Ikemoto,
  author T. Moriwaki, author T. Shikama, author
  K. Takahashi, author
  H. Mori, author H. Nakaya, author T. Sasaki, author Y. Yasui, and author I. Terasaki, title title
  Optical conductivity measurement of a dimer Mott-insulator to charge-order
  phase transition in a two-dimensional quarter-filled organic salt compound,  https://doi.org/10.1103/PhysRevLett.111.217801 journal
  journal Phys. Rev. Lett. volume 111,  pages 217801 (year 2013)NoStop
[Riedl et al.(2021)Riedl,
  Gati, Zielke, Hartmann,
  Vyaselev, Kushch, Jeschke,
  Lang, Valentí, Kartsovnik, and Winter]ried21
  author author K. Riedl, author E. Gati,
  author D. Zielke, author S. Hartmann, author
  O. M. Vyaselev, author
  N. D. Kushch, author
  H. O. Jeschke, author
  M. Lang, author R. Valentí, author M. V.  Kartsovnik, and author S. M.  Winter, title title Spin vortex
  crystal order in organic triangular lattice compound, https://doi.org/10.1103/PhysRevLett.127.147204 journal
  journal Phys. Rev. Lett. volume 127,  pages 147204 (year 2021)NoStop
[Lunkenheimer et al.(2012)Lunkenheimer, Müller, Krohns,
  Schrettle, Loidl, Hartmann,
  Rommel, de Souza, Hotta,
  Schlueter, and Lang]lunk12
  author author P. Lunkenheimer, author J. Müller, author S. Krohns,
  author F. Schrettle, author A. Loidl, author
  B. Hartmann, author
  R. Rommel, author M. de Souza, author C. Hotta, author J. A.  Schlueter, and author M. Lang, title title
  Multiferroicity in an organic charge-transfer salt that is suggestive of
  electric-dipole-driven magnetism, https://doi.org/10.1038/NMAT3400
  journal journal Nat. Mater. volume 11, pages 755 (year 2012)NoStop
[Gati et al.(2018)Gati,
  Fischer, Lunkenheimer, Zielke, Köhler, Kolb, von
  Nidda, Winter, Schubert, Schlueter, Jeschke, Valentí, and  Lang]gati18
  author author E. Gati, author J. K. H. Fischer, author P. Lunkenheimer, author D. Zielke, author S. Köhler,
  author F. Kolb, author
  H.-A. K. von Nidda, author
  S. M. Winter, author
  H. Schubert, author
  J. A. Schlueter, author
  H. O. Jeschke, author
  R. Valentí, and author
  M. Lang, title title Evidence for electronically driven ferroelectricity in a strongly
  correlated dimerized BEDT-TTF molecular conductor, https://doi.org/10.1103/PhysRevLett.120.247601 journal
  journal Phys. Rev. Lett. volume 120,  pages 247601 (year 2018)NoStop
[Kagawa et al.(2013)Kagawa,
  Sato, Miyagawa, Kanoda,
  Tokura, Kobayashi, Kumai,  and Murakami]kaga13
  author author F. Kagawa, author T. Sato,
  author K. Miyagawa, author K. Kanoda, author
  Y. Tokura, author K. Kobayashi, author R. Kumai, and author Y. Murakami, title title
  Charge-cluster glass in an organic conductor, https://doi.org/10.1038/nphys2642 journal journal Nat. Phys. volume 9, pages
  419 (year 2013)NoStop
[Sasaki et al.(2017)Sasaki,
  Hashimoto, Kobayashi, Itoh,
  Iguchi, Nishio, Ikemoto,
  Moriwaki, Yoneyama, Watanabe,
  Ueda, Mori, Kobayashi,
  Kumai, Murakami, Müller,  and Sasaki]sasa17
  author author S. Sasaki, author K. Hashimoto,
  author R. Kobayashi, author K. Itoh, author
  S. Iguchi, author Y. Nishio, author Y. Ikemoto, author T. Moriwaki, author N. Yoneyama, author M. Watanabe, author A. Ueda, author H. Mori, author K. Kobayashi,
  author R. Kumai, author Y. Murakami, author
  J. Müller, and author
  T. Sasaki, title title Crystallization and vitrification of electrons in a glass-forming
  charge liquid, https://doi.org/10.1126/science.aal3120 journal journal Science volume
  357, pages 1381 (year 2017)NoStop
[Kanoda and Kato(2011)]kano11
  author author K. Kanoda and author R. Kato,  title title Mott physics in organic conductors
  with triangular lattices, https://doi.org/10.1146/annurev-conmatphys-062910-140521 journal journal Annu. Rev. Condens. Matter Phys. volume 2, pages 167 (year
  2011)NoStop
[Shimizu et al.(2016)Shimizu, Hiramatsu, Maesato, Otsuka, Yamochi, Ono, Itoh,
  Yoshida, Takigawa, Yoshida,  and Saito]shim16
  author author Y. Shimizu, author T. Hiramatsu,
  author M. Maesato, author A. Otsuka, author
  H. Yamochi, author A. Ono, author M. Itoh, author M. Yoshida,
  author M. Takigawa, author Y. Yoshida, and author
  G. Saito, title title Pressure-tuned exchange coupling of a quantum spin liquid in the
  molecular triangular lattice
  -(ET)_2Ag_2(CN)_3,  https://doi.org/10.1103/PhysRevLett.117.107203 journal
  journal Phys. Rev. Lett. volume 117,  pages 107203 (year 2016)NoStop
[Zhou et al.(2017a)Zhou, Kanoda,  and Ng]kano17
  author author Y. Zhou, author K. Kanoda, and  author T.-K. Ng, title title Quantum spin liquid states, https://doi.org/10.1103/RevModPhys.89.025003 journal
  journal Rev. Mod. Phys. volume 89,  pages 025003 (year 2017a)NoStop
[Shimozawa et al.(2017)Shimozawa, Hashimoto, Ueda, Suzuki, Sugii, Yamada, Imai, Kobayashi, Itoh, Iguchi, Naka, Ishihara, Mori, Sasaki, and Yamashita]shim17
  author author M. Shimozawa, author K. Hashimoto, author A. Ueda,
  author Y. Suzuki, author K. Sugii, author
  S. Yamada, author Y. Imai, author R. Kobayashi, author K. Itoh,
  author S. Iguchi, author M. Naka, author
  S. Ishihara, author
  H. Mori, author T. Sasaki, and author M. Yamashita, title title
  Quantum-disordered state of magnetic and electric dipoles in an organic mott
  system, https://doi.org/10.1038/s41467-017-01849-x journal journal Nat. Comm. volume
  8, pages 1821 (year 2017)NoStop
[Hassan et al.(2018)Hassan,
  Cunningham, Mourigal, Zhilyaeva, Torunova, Lyubovskaya,
  Schlueter, and Drichko]hass18
  author author N. Hassan, author S. Cunningham,
  author M. Mourigal, author E. I. Zhilyaeva, author
  S. A. Torunova, author
  R. N. Lyubovskaya, author
  J. A. Schlueter, and author
  N. Drichko, title title Evidence for a quantum dipole liquid state in an organic
  quasi-two-dimensional material, https://doi.org/10.1126/science.aan6286 journal journal Science volume 360, pages
  1101 (year 2018)NoStop
[Urai et al.(2022)Urai,
  Miyagawa, Watanabe, Zhilyaeva, Torunova, Lyubovskaya,
  Drichko, and Kanoda]urai22
  author author M. Urai, author K. Miyagawa,
  author Y. Watanabe, author E. I. Zhilyaeva, author
  S. A. Torunova, author
  R. N. Lyubovskaya, author
  N. Drichko, and author
  K. Kanoda, title title Anomalously field-susceptible spin clusters emerging in the
  electric-dipole liquid candidate κ-(ET)_2Hg(SCN)_2Br,  https://doi.org/10.1126/sciadv.abn1680 journal
  journal Sci. Adv. volume 8, pages eabn1680 (year 2022)NoStop
[Riedl et al.(2019)Riedl,
  Valentí, and Winter]ried19
  author author K. Riedl, author R. Valentí,  and author S. M. Winter,  title title Critical spin liquid versus
  valence-bond glass in a triangular-lattice organic antiferromagnet, https://doi.org/10.1038/s41467-019-10604-3 journal journal Nat. Comm. volume 10, pages
  2561 (year 2019)NoStop
[Shimizu et al.(2007)Shimizu, Akimoto, Tsujii, Tajima, and Kato]shim07
  author author Y. Shimizu, author H. Akimoto,
  author H. Tsujii, author A. Tajima, and author
  R. Kato, title title Mott transition in a valence-bond solid insulator with a triangular
  lattice, https://doi.org/10.1103/PhysRevLett.99.256403 journal journal Phys. Rev. Lett. volume 99, pages 256403 (year
  2007)NoStop
[Miksch et al.(2021)Miksch,
  Pustogow, Rahim, Bardin,
  Kanoda, Schlueter, Hübner, Scheffler, and Dressel]miks21
  author author B. Miksch, author A. Pustogow,
  author M. J. Rahim, author A. A. Bardin, author
  K. Kanoda, author J. A. Schlueter, author R. Hübner, author M. Scheffler, and author M. Dressel, title title Gapped
  magnetic ground state in quantum spin liquid candidate
  κ-(BEDT-TTF)_2Cu_2(CN)_3, https://doi.org/10.1126/science.abc6363 journal journal Science volume 372, pages
  276 (year 2021)NoStop
[Pustogow(2022)]pust22
  author author A. Pustogow, title title Thirty-year anniversary
  of κ-(BEDT-TTF)_2Cu_2(CN)_3: Reconciling the spin gap in a
  spin-liquid candidate, https://doi.org/10.3390/solids3010007
  journal journal Solids volume 3, pages 93 (year 2022)NoStop
[Powell and McKenzie(2011)]powe11
  author author B. J. Powell and author R. H. McKenzie, title title Quantum frustration in
  organic Mott insulators: from spin liquids to unconventional
  superconductors, https://doi.org/10.1088/0034-4885/74/5/056501
  journal journal Rep. Prog, Phys. volume 74, pages 056501 (year
  2011)NoStop
[Ardavan et al.(2012)Ardavan, Brown, Kagoshima, Kanoda, Kuroki, Mori, Ogata, Uji, and Wosnitza]arda12
  author author A. Ardavan, author S. Brown,
  author S. Kagoshima, author K. Kanoda, author
  K. Kuroki, author H. Mori, author M. Ogata, author S. Uji, and  author J. Wosnitza, title title Recent topics of organic superconductors, https://doi.org/10.1143/JPSJ.81.011004 journal journal J. Phys. Soc. Jpn. volume 81, pages 011004 (year 2012)NoStop
[Clay and Mazumdar(2019)]clay19
  author author R. Clay and author S. Mazumdar, title title From charge- and
  spin-ordering to superconductivity in the organic charge-transfer solids,  https://doi.org/https://doi.org/10.1016/j.physrep.2018.10.006
  journal journal Phys. Rep. volume 788, pages 1 (year 2019)NoStop
[Toyota et al.(2007)Toyota,
  Lang, and Müller]toyo07
  author author N. Toyota, author M. Lang, and  author J. Müller,  @noop  title Low-Dimensional Molecular Metals  (publisher Springer-Verlag Berlin Heidelberg, year
  2007)NoStop
[Ishiguro et al.(1998)Ishiguro, Yamaji, and Saito]ishi98
  author author T. Ishiguro, author K. Yamaji,  and author G. Saito,  @noop  title Organic Superconductors,  edition 2nd ed. (publisher Springer-Verlag,  address Berlin Heidelberg, year 1998)NoStop
[Hotta(2003)]hott03
  author author C. Hotta, title title Classification of quasi-two
  dimensional organic conductors based on a new minimal model, https://doi.org/10.1143/JPSJ.72.840 journal journal J. Phys. Soc. Jpn. volume 72, pages 840 (year 2003)NoStop
[Kandpal et al.(2009)Kandpal, Opahle, Zhang, Jeschke, and Valentí]kand09
  author author H. C. Kandpal, author I. Opahle,
  author Y.-Z. Zhang, author H. O. Jeschke, and author R. Valentí, title title Revision of model parameters for
  -type charge transfer salts: An ab initio study,  https://doi.org/10.1103/PhysRevLett.103.067004 journal
  journal Phys. Rev. Lett. volume 103,  pages 067004 (year 2009)NoStop
[Koretsune and Hotta(2014)]kore14
  author author T. Koretsune and author C. Hotta, title title Evaluating model parameters
  of the - and
  ^-type Mott insulating organic
  solids, https://doi.org/10.1103/PhysRevB.89.045102 journal journal Phys. Rev. B volume
  89, pages 045102 (year 2014)NoStop
[Mori et al.(1999)Mori,
  Mori, and Tanaka]mori99a
  author author T. Mori, author H. Mori, and  author S. Tanaka, title title Structural genealogy of BEDT-TTF-based organic
  conductors II. Inclined molecules: θ, α, and κ
  phases, https://doi.org/10.1246/bcsj.72.179 journal
  journal Bull. Chem. Soc. Jpn. volume
  72, pages 179 (year 1999)NoStop
[Pustogow et al.(2018)Pustogow, Bories, Löhle, Rösslhuber, Zhukova, Gorshunov,
  Tomić, Schlueter, Hübner, Hiramatsu, Yoshida,
  Saito, Kato, Lee,
  Dobrosavljević, Fratini, and  Dressel]pust18
  author author A. Pustogow, author M. Bories,
  author A. Löhle, author R. Rösslhuber, author E. Zhukova, author
  B. Gorshunov, author
  S. Tomić, author J. A. Schlueter, author R. Hübner, author T. Hiramatsu, author Y. Yoshida, author G. Saito, author R. Kato, author T.-H.  Lee, author V. Dobrosavljević, author S. Fratini, and author M. Dressel, title title Quantum spin liquids
  unveil the genuine Mott state, https://doi.org/10.1038/s41563-018-0140-3 journal journal Nat. Mater. volume 17, pages
  773 (year 2018)NoStop
[Zhou et al.(2017b)Zhou, Kanoda,  and Ng]zhou17
  author author Y. Zhou, author K. Kanoda, and  author T.-K. Ng, title title Quantum spin liquid states, https://doi.org/10.1103/RevModPhys.89.025003 journal
  journal Rev. Mod. Phys. volume 89,  pages 025003 (year 2017b)NoStop
[Wietek et al.(2021)Wietek,
  Rossi,  ŠŠimkovic, Klett, Hansmann,
  Ferrero, Stoudenmire, Schäfer, and Georges]wiet21
  author author A. Wietek, author R. Rossi,
  author F.  ŠŠimkovic, author M. Klett, author P. Hansmann,
  author M. Ferrero, author E. M. Stoudenmire, author T. Schäfer, and author A. Georges, title
  title Mott insulating states with competing orders in the
  triangular lattice Hubbard model, https://doi.org/10.1103/PhysRevX.11.041013 journal journal Phys. Rev. X volume 11, pages 041013 (year 2021)NoStop
[Misumi et al.(2017)Misumi,
  Kaneko, and Ohta]misu17
  author author K. Misumi, author T. Kaneko,  and author Y. Ohta, title title Mott transition and magnetism of the
  triangular-lattice Hubbard model with next-nearest-neighbor hopping,  https://doi.org/10.1103/PhysRevB.95.075124 journal
  journal Phys. Rev. B volume 95,  pages 075124 (year 2017)NoStop
[Watanabe et al.(2006)Watanabe, Yokoyama, Tanaka, and  Inoue]wata06
  author author T. Watanabe, author H. Yokoyama,
  author Y. Tanaka, and author J.-i. Inoue, title
  title Superconductivity and a Mott transition in a Hubbard
  model on an anisotropic triangular lattice, https://doi.org/10.1143/JPSJ.75.074707 journal journal J. Phys. Soc. Jpn. volume 75, pages 074707 (year 2006)NoStop
[Ohashi et al.(2008)Ohashi,
  Momoi, Tsunetsugu, and Kawakami]ohas08
  author author T. Ohashi, author T. Momoi,
  author H. Tsunetsugu, and  author N. Kawakami, title title Finite temperature Mott transition in Hubbard
  model on anisotropic triangular lattice, https://doi.org/10.1103/PhysRevLett.100.076402 journal
  journal Phys. Rev. Lett. volume 100,  pages 076402 (year 2008)NoStop
[Oberbauer et al.(2023)Oberbauer, Erkenov, Biberacher,
  Kushch, Gross, and Kartsovnik]ober23
  author author S. Oberbauer, author S. Erkenov,
  author W. Biberacher, author N. D. Kushch, author
  R. Gross, and author
  M. V. Kartsovnik, title
  title Coherent heavy charge carriers in an organic conductor
  near the bandwidth-controlled Mott transition, https://doi.org/10.1103/PhysRevB.107.075139 journal journal Phys. Rev. B volume 107, pages 075139 (year 2023)NoStop
[Brinkman and Rice(1970)]brin70
  author author W. F. Brinkman and author T. M. Rice, title title Application of
  Gutzwiller's variational method to the metal-insulator transition, https://doi.org/10.1103/PhysRevB.2.4302 journal journal Phys. Rev. B volume 2, pages
  4302 (year 1970)NoStop
[Georges et al.(1996)Georges, Kotliar, Krauth, and  Rozenberg]geor96
  author author A. Georges, author G. Kotliar,
  author W. Krauth, and author M. J. Rozenberg, title title Dynamical mean-field theory of strongly correlated
  fermion systems and the limit of infinite dimensions, https://doi.org/10.1103/RevModPhys.68.13 journal journal Rev. Mod. Phys. volume 68, pages 13 (year 1996)NoStop
[Wosnitza(1996)]wosn96
  author author J. Wosnitza, @noop  title Fermi Surfaces of
  Low-Dimensional Organic Metals and Superconductors (publisher
  Springer-Verlag, address Berlin Heidelberg, year
  1996)NoStop
[Singleton(2000)]sing00
  author author J. Singleton, title title Studies of
  quasi-two-dimensional organic conductors based on BEDT-TTF using high
  magnetic fields, https://doi.org/10.1088/0034-4885/63/8/201
  journal journal Rep. Prog. Phys. volume 63, pages 1111 (year
  2000)NoStop
[Kartsovnik(2004)]kart04
  author author M. V. Kartsovnik, title title High magnetic fields:
  A tool for studying electronic properties of layered organic metals, https://doi.org/10.1021/cr0306891 journal journal Chem. Rev. volume 104, pages
  5737 (year 2004)NoStop
[Audouard et al.(2016)Audouard, Fortin, Vignolles, Laukhin, Kushch, and Yagubskii]audo16
  author author A. Audouard, author J.-Y. Fortin, author D. Vignolles,
  author V. N. Laukhin, author N. D. Kushch, and author E. B. Yagubskii, title title New insights on frequency combinations and
  `forbidden frequencies' in the de Haas–van Alphen spectrum of
  κ-(ET)_2Cu(SCN)_2, https://doi.org/10.1088/0953-8984/28/27/275702 journal
  journal J. Phys.: Condens. Matter volume
  28, pages 275702 (year 2016)NoStop
[sm-()]sm-hp
  @noop  note See Supplemental Material at [URL will be
  inserted by publisher] for a brief account of the SdH oscillations in
  κ-NCS, description and examples of the cyclotron mass evaluation, and
  for fitting the P-dependent mass m_c,β in κ-NCS with
  Eq. (3). The Supplemental Material also includes Refs.
  <cit.>NoStop
[Caulfield et al.(1994)Caulfield, Lubczynski, Pratt, Singleton, Ko, Hayes, Kurmoo, and Day]caul94
  author author J. Caulfield, author W. Lubczynski, author F. L. Pratt, author J. Singleton,
  author D. Y. K. Ko, author W. Hayes, author
  M. Kurmoo, and author
  P. Day, title title Magnetotransport studies of the organic superconductor
  κ-(BEDT-TTF)_2Cu(NCS)_2 under pressure: the relationship between
  carrier effective mass and critical temperature, https://doi.org/10.1088/0953-8984/6/15/013 journal journal J. Phys.: Condens. Matter volume 6,  pages 2911 (year 1994)NoStop
[Pratt(2010)]prat10b
  author author F. L. Pratt, title title Using Shubnikov - de Haas
  data to estimate the magnetic frustration parameter t'/t in the spin-liquid
  system κ-ET_2Cu_2(CN)_3, https://doi.org/https://doi.org/10.1016/j.physb.2010.01.125 journal journal Physica B volume
  405, pages S205 (year 2010)NoStop
[Williams et al.(1990)Williams, Kini, Wang, Carlson, Geiser, Montgomery, Pyrka, Watkins, and Kommers]will90
  author author J. M. Williams, author A. M. Kini,
  author H. H. Wang, author K. D. Carlson, author
  U. Geiser, author L. K. Montgomery, author G. J. Pyrka, author D. M.  Watkins, and author J. M.  Kommers, title title From
  semiconductor-semiconductor transition (42 K) to the highest-T_c
  organic superconductor, κ-(ET)_2Cu[N(CN)_2]Cl (T_c =
  12.54 K), https://doi.org/10.1021/ic00343a003 journal journal Inorg. Chem. volume
  29, pages 3272 (year 1990)NoStop
[Urayama et al.(1988)Urayama, Yamochi, Saito, Nozawa, Sugano, Kinoshita, Sato, Oshima, Kawamoto, and Tanaka]uray88
  author author H. Urayama, author H. Yamochi,
  author G. Saito, author K. Nozawa, author
  T. Sugano, author M. Kinoshita, author S. Sato, author K. Oshima, author A. Kawamoto,  and author J. Tanaka,  title title A new ambient pressure organic
  superconductor based on bedt-ttf with tc higher than 10 k (tc=10.4 k),  https://doi.org/10.1246/cl.1988.55 journal journal Chemistry Letters volume 17, pages 55 (year 1988)NoStop
[Müller and Ueba(1993)]muel93
  author author H. Müller and author Y. Ueba, title title A facile synthesis of
  bis(ethylenedithio)tetrathiafulvalene, https://doi.org/10.1055/s-1993-25953 journal journal Synthesis volume 9, pages
  853 (year 1993)NoStop
[Müller et al.(1997)Müller, Jouan, and Salhi]muel97
  author author H. Müller, author C. Jouan,  and author F. Salhi, title title BEDT-TTF and related donor molecules - made
  easy, https://doi.org/https://doi.org/10.1016/S0379-6779(97)80314-1 journal journal Synth. Metals volume
  85, pages 1457 (year 1997)NoStop
[Müller and Bourcet(2022)]muel22
  author author H. Müller and author L. Bourcet, title title
  [1,3]-dithiolo-[4,5-d][1,3-dithiole]-2,5-dione, https://doi.org/10.1055/s-0040-1720891 journal journal Synthesis volume 54, pages
  1817 (year 2022)NoStop
[Nomura et al.(1979)Nomura,
  Yamamoto, Ochiai, and Fujiwara]nomu79
  author author M. Nomura, author Y. Yamamoto,
  author Y. Ochiai, and author H. Fujiwara, title
  title The measurement of the resistance of manganin wire with
  the cubic-anvil type pressure apparatus, https://doi.org/10.1143/JJAP.18.363 journal journal Jpn. J. Appl. Phys. volume 18, pages 363 (year 1979)NoStop
[Kartsovnik et al.(1995)Kartsovnik, Biberacher, Andres, and  Kushch]kart95c
  author author M. V. Kartsovnik, author W. Biberacher, author K. Andres,  and author N. D. Kushch,  title title Shubnikov-de Haas effect in the
  organic superconductor κ-(BEDT-TTF)_2Cu[N(CN)_2]Cl under
  pressure, http://jetpletters.ru/ps/1222/article_18475.shtml
  journal journal JETP Lett. volume 62, pages 905 (year 1995)NoStop
[Yamauchi et al.(1996)Yamauchi, Kartsovnik, Ishiguro,
  Kubota, and Saito]yama96
  author author Y. Yamauchi, author M. V. Kartsovnik, author T. Ishiguro, author M. Kubota,  and author G. Saito, title title Angle-dependent magnetoresistance and
  Shubnikov-de Haas oscillations in the organic superconductor
  κ-(BEDT-TTF)_2Cu[N(CN)_2]Cl under pressure, https://doi.org/10.1143/JPSJ.65.354 journal journal J. Phys. Soc. Jpn. volume 65, pages 354 (year 1996)NoStop
[Com()]Comment_MB
  @noop  note The inversion symmetry of the crystal
  structure of κ-Cl <cit.> implies no gap between the open
  Fermi sheets and the α pocket. However, a small gap,
  Δ_MB≃ 1.6 meV, has been predicted to arise due to the
  spin-orbit interaction <cit.>, which is fully consistent with the
  experimental estimation, see Supplemental Material for Ref.
  <cit.>.Stop
[Kartsovnik et al.(1988)Kartsovnik, Kononovich, Laukhin, and  Schegolev]kart88b
  author author M. V. Kartsovnik, author P. A. Kononovich, author V. N. Laukhin, and author I. F. Schegolev, title title Anisotropy of
  magnetoresistance and the Shubnikov-de Haas oscillations in the organic
  metal β-(ET)_2IBr_2, http://jetpletters.ru/ps/0/article_16777.shtml journal
  journal JETP Lett. volume 48,  pages 541 (year 1988)NoStop
[Kang et al.(1989)Kang,
  Montambaux, Cooper, Jérome, Batail, and Lenoir]kang89
  author author W. Kang, author G. Montambaux,
  author J. R. Cooper, author D. Jérome, author
  P. Batail, and author
  C. Lenoir, title title Observation of giant magnetoresistance oscillations in the
  high-T, phase of the two-dimensional organic conductor
  β-(BEDT-TTF)_2I_3, https://doi.org/10.1103/PhysRevLett.62.2559 journal journal Phys. Rev. Lett. volume 62, pages 2559 (year 1989)NoStop
[Weiss et al.(1999a)Weiss, Kartsovnik, Biberacher, Steep,
  Balthes, Jansen, Andres,  and Kushch]weis99a
  author author H. Weiss, author M. V. Kartsovnik, author W. Biberacher, author E. Steep,
  author E. Balthes, author A. Jansen, author
  K. Andres, and author
  N. Kushch, title title Magnetotransport studies of the Fermi surface in the organic
  superconductor κ-(BEDT-TTF)_2Cu[N(CN)_2]Br, https://doi.org/10.1103/PhysRevB.59.12370 journal journal Phys. Rev. B volume 59, pages 12370 (year 1999a)NoStop
[Schiller et al.(2000)Schiller, Schmidt, Balthes, Schweitzer, Koo, Whangbo, Heinen, Klausa, Kircher, and  Strunz]schi00
  author author M. Schiller, author W. Schmidt,
  author E. Balthes, author D. Schweitzer, author
  H. Koo, author M. H. Whangbo, author I. Heinen, author T. Klausa, author P. Kircher, and author W. Strunz, title title
  Investigations of the Fermi surface of a new organic metal:
  (BEDT-TTF)_4[ Ni(dto)_2], https://dx.doi.org/10.1209/epl/i2000-00329-2 journal
  journal Europhys. Lett. volume 51,  pages 82 (year 2000)NoStop
[Bergemann et al.(2000)Bergemann, Julian, Mackenzie, Nishizaki, and Maeno]berg00
  author author C. Bergemann, author S. R. Julian, author A. P. Mackenzie, author S. Nishizaki, and author Y. Maeno, title title Detailed topography of the
  Fermi surface of Sr_2RuO_4, https://doi.org/10.1103/PhysRevLett.84.2662 journal journal Phys. Rev. Lett. volume 84, pages 2662 (year 2000)NoStop
[Carrington(2011)]carr11
  author author A. Carrington, title title Quantum oscillation
  studies of the Fermi surface of iron-pnictide superconductors, http://stacks.iop.org/0034-4885/74/i=12/a=124507 journal
  journal Rep. Prog. Phys. volume 74,  pages 124507 (year 2011)NoStop
[Sebastian and Proust(2015)]seba15
  author author S. E. Sebastian and author C. Proust, title title Quantum oscillations in
  hole-doped cuprates, https://doi.org/10.1146/annurev-conmatphys-030212-184305 journal journal Annu. Rev. Condens. Matter Phys. volume 6, pages 411 (year
  2015)NoStop
[Oliviero et al.(2022)Oliviero, Benhabib, Gilmutdinov,
  Vignolle, Drigo, Massoudzadegan, Leroux, Rikken,
  Forget, Colson, Vignolles,  and Proust]oliv22
  author author V. Oliviero, author S. Benhabib,
  author I. Gilmutdinov, author B. Vignolle, author
  L. Drigo, author M. Massoudzadegan, author M. Leroux, author G. L. J. A.  Rikken, author A. Forget, author D. Colson,
  author D. Vignolles, and  author C. Proust, title title Magnetotransport signatures of antiferromagnetism
  coexisting with charge order in the trilayer cuprate
  HgBa_2Ca_2Cu_3O_8+δ, https://doi.org/10.1038/s41467-022-29134-6 journal journal Nat. Comm. volume 13, pages
  1568 (year 2022)NoStop
[Eaton et al.(2024)Eaton,
  Weinberger, Popiel, Wu,
  Hickey, Cabala, Pospís̆il, Prokles̆ka, Haidamak,
  Bastien, Opletal, Sakai,
  Haga, Nowell, Benjamin,
  Sechovský, Lonzarich, Grosche, and Valis̆ka]eato24
  author author A. G. Eaton, author T. I. Weinberger, author N. J. M. Popiel, author Z. Wu, author A. J. Hickey, author
  A. Cabala, author J. Pospís̆il, author J. Prokles̆ka, author T. Haidamak, author G. Bastien, author P. Opletal, author H. Sakai, author Y. Haga, author R. Nowell, author S. M. Benjamin, author V. Sechovský, author G. G. Lonzarich, author F. M. Grosche, and author M. Valis̆ka, title title Quasi-2D Fermi
  surface in the anomalous superconductor UTe_2, https://doi.org/10.1038/s41467-023-44110-4 journal journal Nat. Comm. volume 15, pages
  223 (year 2024)NoStop
[com(a)]comm_PhSh
  @noop    note When the Landau-level
  spacing becomes comparable to the interlayer transfer integral, the beats of
  SdH oscillations acquire an additional field-dependent phase shift, which
  breaks the exact 1/B-periodicity <cit.>. In the layered
  metal β-(BEDT-TTF)_2IBr_2 displaying a similar anisotropy, the beat
  phase is shifted by about 10% of the period at B ∼ 15 T
  <cit.>. Thus, a straightforward estimation of the Fermi surface
  warping from the positions of two beat nodes leads to an error ≲
  10%.Stop
[Singleton et al.(2002)Singleton, Goddard, Ardavan, Harrison, Blundell, Schlueter, and  Kini]sing02
  author author J. Singleton, author P. A. Goddard, author A. Ardavan,
  author N. Harrison, author S. J. Blundell, author
  J. A. Schlueter, and author
  A. M. Kini, title title Test for interlayer coherence in a quasi-two-dimensional
  superconductor, https://doi.org/10.1103/PhysRevLett.88.037001
  journal journal Phys. Rev. Lett. volume 88, pages 037001 (year
  2002)NoStop
[Shoenberg(1984)]shoe84
  author author D. Shoenberg, @noop  title Magnetic Oscillations
  in Metals (publisher Cambridge University Press, address Cambridge, year 1984)NoStop
[Wosnitza et al.(1992)Wosnitza, Crabtree, Wang, Geiser, Williams, and Carlson]wosn92
  author author J. Wosnitza, author G. W. Crabtree, author H. H. Wang,
  author U. Geiser, author J. M. Williams, and author K. D. Carlson, title title de haas–van alphen studies of the organic
  superconductors α-(ET)_2NH_4Hg(SCN)_4 and
  κ-(ET)_2Cu(NCS)_2 [with ET =
  bis(ethelenedithio)-tetrathiafulvalene], https://doi.org/10.1103/PhysRevB.45.3018 journal journal Phys. Rev. B volume 45, pages 3018 (year 1992)NoStop
[Kovalev et al.(1993)Kovalev, Kartsovnik, and Kushch]kova93
  author author A. E. Kovalev, author M. V. Kartsovnik, and author N. D. Kushch, title title Quantum and semi-classical
  magnetoresistance oscillaitons in a new organic metal
  (BEDT-TTF)_2TlHg(SeCN)_4, @noop  journal
  journal Solid State Commun. volume
  87, pages 705 (year 1993)NoStop
[Meyer et al.(1995)Meyer,
  Steep, Biberacher, Christ,
  Lerf, Jansen, Joss,
  Wyder, and Andres]meye95
  author author F. A. Meyer, author E. Steep,
  author W. Biberacher, author P. Christ, author
  A. Lerf, author A. G. M. Jansen, author W. Joss, author P. Wyder, and author K. Andres, title title High-field de Haas-van
  Alphen studies of κ-(BEDT-TTF)_2Cu(NCS)_2, https://doi.org/10.1209/0295-5075/32/8/011 journal journal Europhys. Lett. volume 32, pages 681 (year 1995)NoStop
[Weiss et al.(1999b)Weiss, Kartsovnik, Biberacher, Balthes,
  Jansen, and Kushch]weis99b
  author author H. Weiss, author M. V. Kartsovnik, author W. Biberacher, author E. Balthes,
  author A. G. M. Jansen, and  author N. D. Kushch, title title Angle-dependent magnetoquantum oscillations in
  κ-(BEDT-TTF)_2Cu[N(CN)_2]Br, https://doi.org/10.1103/PhysRevB.60.R16259 journal journal Phys. Rev. B volume 60, pages R16259 (year 1999b)NoStop
[Sasaki and Fukase(1999)]sasa99
  author author T. Sasaki and author T. Fukase, title title Spin splitting at the
  high-magnetic-field phase transition of the organic conductor α-(BEDT-TTF)_2KHg(SCN)_4, https://doi.org/10.1103/PhysRevB.59.13872 journal journal Phys. Rev. B volume 59, pages 13872 (year 1999)NoStop
[Wosnitza et al.(2008)Wosnitza, Gvozdikov, Hagel, Ignatchik, Bergk, Meeson, Schlueter, Davis, Winter, and  Gard]wosn08
  author author J. Wosnitza, author V. M. Gvozdikov, author J. Hagel,
  author O. Ignatchik, author B. Bergk, author
  P. J. Meeson, author
  J. A. Schlueter, author
  H. Davis, author R. W. Winter, and author G. L. Gard, title title
  Spin-zero anomaly in the magnetic quantum oscillations of a two-dimensional
  metal, https://doi.org/10.1088/1367-2630/10/8/083032 journal journal New J. Phys. volume
  10, pages 083032 (year 2008)NoStop
[Yamaji(1989)]yama89
  author author K. Yamaji, title title On the angle dependence of
  the magnetoresistance in quasi-two-dimensional organic superconductors,  @noop  journal journal J. Phys. Soc.
  Jpn. volume 58, pages 1520 (year 1989)NoStop
[Kartsovnik et al.(1990)Kartsovnik, Kononovich, Laukhin,
  Pesotskii, and Schegolev]kart90
  author author M. V. Kartsovnik, author P. A. Kononovich, author V. N. Laukhin, author S. I. Pesotskii, and author I. F. Schegolev, title title Galvanomagnetic
  properties and the Fermi surface of the organic superconductor
  β-(ET)_2IBr_2, http://jetp.ras.ru/cgi-bin/e/index/e/70/4/p735?a=list journal
  journal Sov. Phys. JETP volume 70,  pages 735 (year 1990)NoStop
[Wosnitza et al.(1993)Wosnitza, Crabtree, Williams, Wang, Carlson, and Geiser]wosn93
  author author J. Wosnitza, author G. W. Crabtree, author J. M. Williams, author H. H. Wang,
  author K. D. Carlson, and  author U. Geiser, title title De Haas - van Alphen studies and Fermi surface
  properties of organic superconductors (ET)_2X, https://doi.org/10.1016/0379-6779(93)90052-X journal
  journal Synth. Met. volume 55-57,  pages 2891 (year 1993)NoStop
[Peschansky(2002)]pesc02
  author author V. G. Peschansky, title title Galvanomagnetic
  phenomena in organic layered conductors, https://doi.org/10.1134/1.1484997 journal journal JETP volume 94, pages 1035
  (year 2002)NoStop
[Kartsovnik(2008)]kart08a
  author author M. V. Kartsovnik, title title Layered organic
  conductors in strong magnetic fields, in @noop  booktitle The Physics of Organic Superconductors and Conductors,  editor edited by editor A. G.  Lebed (publisher Springer Verlag, address Berlin Heidelberg, year 2008) pp. pages 185–246NoStop
[Watanabe et al.(1999)Watanabe, Nogami, Oshima, Ito, Ishiguro, and Saito]wata99
  author author M. Watanabe, author Y. Nogami,
  author K. Oshima, author H. Ito, author
  T. Ishiguro, and author
  G. Saito, title title Low temperature superstructure and transfer integrals in
  κ-(BEDT-TTF)_2Cu[N(CN)_2]X: X = Cl, Br, https://doi.org/https://doi.org/10.1016/S0379-6779(98)00615-8 journal journal Synt. Metals volume
  103, pages 1909 (year 1999)NoStop
[Schultz et al.(1991)Schultz, Beno, Geiser, Wang, Kini, Williams, and Whangbo]schu91
  author author A. J. Schultz, author M. A. Beno,
  author U. Geiser, author H. Wang, author
  A. M. Kini, author
  J. M. Williams, and author
  M.-H. Whangbo, title
  title Single-crystal X-ray and neutron diffraction
  investigations of the temperature dependence of the structure of the T_c
  = 10 K organic superconductor κ-(ET)_2Cu(NCS)_2, https://doi.org/https://doi.org/10.1016/0022-4596(91)90201-R journal journal J. Solid State Chem. volume 94, pages 352  (year
  1991)NoStop
[com(b)]comm_F0
  @noop   note For the κ-Cl salt
  the zero-pressure value was estimated from the linear extrapolation of the
  F_β(p) data in the p interval 20 to 200 MPa, see
  inset in Fig. <ref>(a).Stop
[Schultz et al.(1994)Schultz, Wang, Williams, Finger, Hazen, Rovira, and Whangbo]schu94
  author author A. J. Schultz, author H. H. Wang,
  author J. M. Williams, author L. W. Finger, author
  R. M. Hazen, author
  C. Rovira, and author
  M.-H. Whangbo, title
  title X-ray diffraction and electronic band structure study of
  the organic superconductor κ-(ET)_2Cu[N(CN)_2]Cl at pressures up
  to 28 kbar, https://doi.org/https://doi.org/10.1016/0921-4534(94)90577-0 journal journal Physica C: Supercond. volume 234, pages 300  (year
  1994)NoStop
[Rahal et al.(1997)Rahal,
  Chasseau, Gaultier, Ducasse,
  Kurmoo, and Day]raha97
  author author M. Rahal, author D. Chasseau,
  author J. Gaultier, author L. Ducasse, author
  M. Kurmoo, and author
  P. Day, title title Isothermal compressibility and pressure dependence of the crystal
  structures of the superconducting charge-transfer salt
  κ-(BEDT-TTF)_2Cu(NCS)_2 [BEDT-TTF =
  bis(ethylenedithio)tetrathiafulvalene], https://doi.org/10.1107/S0108768195012122 journal journal Acta Crystallogr. volume B53, pages 159 (year 1997)NoStop
[Lifshitz and Kosevich(1956)]lifs55
  author author I. M. Lifshitz and author A. M. Kosevich, title title Theory of magnetic
  susceptibility in metals at low temperatures, http://jetp.ras.ru/cgi-bin/e/index/e/2/4/p636?a=list journal
  journal Sov. Phys. JETP volume 2,  pages 636 (year 1956)NoStop
[Merino and McKenzie(2000)]meri00a
  author author J. Merino and author R. H. McKenzie, title title Cyclotron effective
  masses in layered metals, https://doi.org/10.1103/PhysRevB.62.2416
  journal journal Phys. Rev. B volume 62, pages 2416 (year
  2000)NoStop
[Semeniuk et al.(2023)Semeniuk, Chang, Baglo, Friedemann, Tozer, Coniglio, Gamża, Reiss, Alireza, Leermakers, McCollam, Grockowiak, and  Grosche]seme23
  author author K. Semeniuk, author H. Chang,
  author J. Baglo, author S. Friedemann, author
  S. W. Tozer, author
  W. A. Coniglio, author
  M. B. Gamża, author
  P. Reiss, author P. Alireza, author I. Leermakers, author A. McCollam, author A. D.  Grockowiak, and author F. M.  Grosche, title title Truncated
  mass divergence in a Mott metal, https://doi.org/10.1073/pnas.2301456120 journal journal Proc. Natl. Acad. Sci. USA volume 120,  pages e2301456120 (year 2023)NoStop
[com(c)]comm_rang
  @noop   note Three lowest-pressure
  points for κ-Cl, taken at p < 40 MPa, were excluded from fitting. These
  points belong to the phase-coexistence region of the phase diagram, where an
  anomalous acceleration of the pressure dependence is observed <cit.>.
  Consistently, these lie above the fitting curve.Stop
[Com()]Comment_mass
  @noop  note The band cyclotron mass is ultimately
  determined by the electron density of states on the Fermi level
  <cit.>, which is quite sensitive to the details of the band-structure
  calculations and may differ by up to 30% in different works, cf., e.g.,
  Refs. <cit.> and <cit.>.Stop
[Zverev et al.(2019)Zverev,
  Biberacher, Oberbauer, Sheikin, Alemany, Canadell, and  Kartsovnik]zver19
  author author V. N. Zverev, author W. Biberacher,
  author S. Oberbauer, author I. Sheikin, author
  P. Alemany, author E. Canadell, and author M. V. Kartsovnik, title title
  Fermi surface properties of the bifunctional organic metal
  -(BETS)_2Mn[N(CN)_2]_3
  near the metal-insulator transition, https://doi.org/10.1103/PhysRevB.99.125136 journal journal Phys. Rev. B volume 99, pages 125136 (year 2019)NoStop
[com()]comm_caul-
  @noop  note Our data on the α mass in κ-NCS is
  about 10% lower than reported by Caulfield et al. <cit.>. While the
  reason for the discrepancy between the two datasets is not clear, both
  exhibit essentially the same pressure dependence.Stop
[Goddard et al.(2004)Goddard, Blundell, Singleton, McDonald, Ardavan, Narduzzo, Kini, and Sasaki]godd04
  author author P. A. Goddard, author S. J. Blundell, author J. Singleton,
  author R. D. McDonald, author A. Ardavan, author
  A. Narduzzo, author
  J. A. S. A. M. Kini, and author T. Sasaki, title
  title Angle-dependent magnetoresistance of the layered organic
  superconductor κ-(ET)_2(NCS)_2: Simulation and experiment,  @noop  journal journal Phys. Rev. B  volume 69, pages 174509 (year 2004)NoStop
[Gutman and Maslov(2008)]gutm08
  author author D. B. Gutman and author D. L. Maslov, title title Boson-assisted tunneling
  in layered metals, https://doi.org/10.1103/PhysRevB.77.035115
  journal journal Phys. Rev. B volume 77, pages 035115 (year
  2008)NoStop
[Ho and Schofield(2005)]ho05
  author author A. F. Ho and author A. J. Schofield, title title c-axis transport in
  highly anisotropic metals: Role of small polarons, https://doi.org/10.1103/PhysRevB.71.045101 journal journal Phys. Rev. B volume 71, pages 045101 (year 2005)NoStop
[Analytis et al.(2006)Analytis, Ardavan, Blundell, Owen, Garman, Jeynes, and Powell]anal06
  author author J. G. Analytis, author A. Ardavan,
  author S. J. Blundell, author R. L. Owen, author
  E. F. Garman, author
  C. Jeynes, and author
  B. J. Powell, title
  title Effect of irradiation-induced disorder on the conductivity
  and critical temperature of the organic superconductor
  -(BEDT-TTF)_2Cu(SCN)_2,  https://doi.org/10.1103/PhysRevLett.96.177002 journal
  journal Phys. Rev. Lett. volume 96,  pages 177002 (year 2006)NoStop
[Hiramatsu et al.(2015)Hiramatsu, Yoshida, Saito, Otsuka, Yamochi, Maesato, Shimizu, Ito, and Kishida]hira15
  author author T. Hiramatsu, author Y. Yoshida,
  author G. Saito, author A. Otsuka, author
  H. Yamochi, author M. Maesato, author Y. Shimizu, author H. Ito, and author H. Kishida, title title Quantum
  spin liquid: design of a quantum spin liquid next to a superconducting state
  based on a dimer-type ET Mott insulator, https://doi.org/10.1039/C4TC01701C journal journal J. Mater. Chem. C volume 3, pages 1378 (year 2015)NoStop
[Winter et al.(2017)Winter,
  Riedl, and Valentí]wint17
  author author S. M. Winter, author K. Riedl, and  author R. Valentí,  title title Importance of spin-orbit coupling in
  layered organic salts, https://doi.org/10.1103/PhysRevB.95.060404
  journal journal Phys. Rev. B volume 95, pages 060404 (year
  2017)NoStop
[Grigoriev et al.(2002)Grigoriev, Kartsovnik, Biberacher,
  Kushch, and Wyder]grig02b
  author author P. D. Grigoriev, author M. V. Kartsovnik, author W. Biberacher, author N. D. Kushch, and author P. Wyder, title title Anomalous beating phase of
  the oscillating interlayer magnetoresistance in layered metals, https://doi.org/10.1103/PhysRevB.65.060403 journal journal Phys. Rev. B volume 65, pages 060403(R) (year 2002)NoStop
[Grigoriev(2003)]grig03
  author author P. D. Grigoriev, title title Theory of the
  Shubnikov–de Haas effect in quasi-two-dimensional metals, https://doi.org/10.1103/PhysRevB.67.144401 journal journal Phys. Rev. B volume 67, pages 144401 (year 2003)NoStop
[Xu et al.(1995)Xu,
  Ching, Jean, and Lou]xu95
  author author Y.-N. Xu, author W. Y. Ching,
  author Y. C. Jean, and  author Y. Lou, title title First-principles calculation of the electronic and
  optical properties of the organic superconductor
  κ-(BEDT-TTF)_2Cu(NCS)_2, https://doi.org/10.1103/PhysRevB.52.12946 journal journal Phys. Rev. B volume 52, pages 12946 (year 1995)NoStop
[Ferber et al.(2014)Ferber,
  Foyevtsova, Jeschke, and Valentí]ferb14
  author author J. Ferber, author K. Foyevtsova,
  author H. O. Jeschke, and  author R. Valentí,  title title Unveiling the microscopic nature of
  correlated organic conductors: The case of κ-(BEDT-TTF)_2Cu[N(CN)_2]Br_xCl_1-x, https://doi.org/10.1103/PhysRevB.89.205106 journal journal Phys. Rev. B volume 89, pages 205106 (year 2014)NoStop

