# Interplay between Vortex Dynamics and Superconducting Gap Structure in Layered Organic Superconductors

## Abstract

**:**

_{2}Cu(NCS)

_{2}, β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, and λ-(BETS)

_{2}GaCl

_{4}. The interplay between the vortex dynamics and nodal structures is discussed for these superconductors.

## 1. Introduction

^{−}. Figure 1a shows schematic structure of ET (or BETS) donor conducting layers and anion insulating layers in a layered organic conductor, where BETS denotes bis(ethylenedithio)tetraselenafulvalene. The molecular structures of ET and BETS are shown in the upper right side of Figure 1a. In layered organic superconductors, there are several types (labeled by Greek letters) in packed ET donor layers. The k-, β″-, and λ-type arrangements in donor layers are shown in Figure 1b–d. In the k type compounds, k-(ET)

_{2}X, the measurements of Shubnikov-de Haas (SdH) and de Haas-van Alphen (dHvA) oscillations have elucidated the presence of a well-defined Fermi surface (FS) with simple structures [2]. Moreover. the moderately heavy effective mass revealed by SdH and dHvA experiments suggests that electron correlation plays a significant role on determining the physical properties of the normal state as well as superconducting (SC) state. It was suggested that superconductivity appears in proximity to the antiferromagnetic insulating state in the electronic phase diagram [3,4]. Since some of these unusual physical properties suggest similarities with high-T

_{c}cuprates, many researchers have pointed out that the spin fluctuations play a vital role for the appearance of SC state [5,6,7,8].

_{xy}(with nodes along vertical and horizontal directions) differs from d

_{x}

^{2}

_{−y}

^{2}(diagonal direction) only in the location of the line nodes (π/4 rotation of the latter becomes identical with the former). Therefore, direction-sensitive experimental methods are highly needed to distinguish between these gap structures. Since the SC gap structure is intimately associated with the pairing mechanism [16], it is of fundamental importance to elucidate the SC gap structure.

_{2}Cu(NCS)

_{2}, β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, and λ-(BETS)

_{2}GaCl

_{4}[25,26,27]. SC parameters for these superconductors are listed in Table 1. As shown below, we clearly observed the flux-flow resistivity with fourfold-symmetric anisotropy, owning to the d-wave SC gap symmetry in k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}. On the other hand, twofold symmetric anisotropy was found in λ-(BETS)

_{2}GaCl

_{4}although λ-(BETS)

_{2}GaCl

_{4}possesses the similar FS and SC gap structures in the former two superconductors. Interplay between in-plane anisotropy of vortex dynamics and nodal SC gap structures for these superconductors are discussed below.

## 2. Experimental Methods

_{2}Cu(NCS)

_{2}, β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, and λ-(BETS)

_{2}GaCl

_{4}were synthesized electrochemically. The interlayer resistance was measured by a four-terminal ac method, where the electric current is parallel to the least conducting direction. To investigate the in-plane angular variation of the flux-flow resistance for layered organic superconductors, it is crucial to rotate applied field parallel to the conducting layers with high accuracy because a slight field-angle misalignment gives rise to twofold anisotropy of the magnetoresistance related to the huge H

_{c2}anisotropy [33]. To check the reproducibility, four samples were simultaneously mounted on a two-axis rotator in a

^{4}He cryostat with a 17-T SC magnet. By using the rotator, it is possible to sweep the θ angle with a resolution of ∆θ = 0.1°, where θ is the polar angle between the least conducting axis and magnetic field direction. In addition, we can discretely control the plane of rotation, which is represented by the azimuthal angle ϕ with intervals of ∆ϕ = 5° or 10 within the conducting layers.

_{2}Cu(NCS)

_{2}is shown in Figure 2a [25]. For the magnetic field exactly applied parallel to the conducting plane, the ρ(θ) curve shows a sharp drop due to the SC transition at the lowest current density of 0.5 mA/cm

^{2}. It is remarkable that the resistivity at θ = 90° depends strongly on the current density. A sharp peak is clearly observed at θ = 90° for highest current density of 100 mA/cm

^{2}. The resistivity for |θ − 90°| > 5° is independent of current density of up to 100 mA/cm

^{2}. Thus, the effect of Joule heating is negligibly small. Instead, the sharp peaks are due to the vortex dynamics [25,33,34,35,36,37,38]. Similar features are found for β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}in Figure 2b and λ-(BETS)

_{2}GaCl

_{4}in Figure 2c [26,27].

## 3. Results and Discussion

#### 3.1. κ-(ET)_{2}Cu(NCS)_{2}

_{2}X possesses similar features to that of high-T

_{c}cuprates, such as quasi-2D electronic structure and the competition of its SC phase with the antiferromagnetic insulating phase [2,3,4]. To elucidate the pairing mechanism in the k-(ET)

_{2}X system, its SC gap symmetry has been extensively investigated from both experimental and theoretical points of view [9,10,11,12,13,14]. Various experiments such as NMR [9], heat capacity [10,11], and mm-wave transmission measurements [12] suggested presence of d-wave SC gap in k-(ET)

_{2}Cu(NCS)

_{2}. As for the nodal direction, scanning tunneling microscopy (STM) [13] and thermal conductivity experiments [14] suggested the line node gap rotated 45° relative to the b and c axes (d

_{x}

^{2}

_{−y}

^{2}symmetry). Malone et al. [15] argued in favor of d

_{xy}symmetry (the line nodes along the b and c axes) from the heat capacity measurement. These results have demonstrated the d-wave superconductivity in the k-(ET)

_{2}X system, but the location of gap nodes is still controversial. In this section, we present in-plane anisotropy of upper critical field and vortex flow resistivity for k-(ET)

_{2}Cu(NCS)

_{2}and discuss the nodal structure.

#### 3.1.1. In-Plane Anisotropy of Upper Critical Field in k-(ET)_{2}Cu(NCS)_{2}

_{J}, a “midpoint” T

_{M}, “a zero resistance extrapolation” T

_{X}(ignoring the tail near R = 0), and “zero resistance point” T

_{Z}are defined. A similar fashion was confirmed for ϕ = 45° and ϕ = 0° (H //

**c**).

_{c2}in spite of many suggestions of d-wave pairing symmetry in k-(ET)

_{2}Cu(NCS)

_{2}. This is consistent with previous magnetoresistance study by Nam et al. [39]. Lower temperatures will be needed for confirmation of an expected d-wave nature in H

_{c2}. In addition, we find change of slope in H

_{c2}line near T

_{c}, suggesting the dimensional crossover from anisotropic 3D SC to Josephson coupled 2D SC state [40,41,42]. It means that despite short coherence length along the interlayer direction, the SC state can be regarded as anisotropic 3D SC state only near H

_{c2}line.

#### 3.1.2. In-Plane Anisotropy of Vortex Dynamics in k-(ET)_{2}Cu(NCS)_{2}

_{c2}(ϕ) ∝ cos4ϕ in the d-wave superconductivity [43,44,45]. The ρ(ϕ) curves are naively consistent with this theory; the maximum and minimum of H

_{c2}give the minimum and maximum resistivities, respectively. When d

_{x}

^{2}

_{−y}

^{2}pairing is assumed, H

_{c2}(ϕ) has maxima at ϕ = 0° (H // c) and ϕ = 90° (H // b), and a minimum at ϕ = 45°, whereas d

_{xy}pairing leads to H

_{c2}with maxima and minima reversed with respect to d

_{x}

^{2}

_{−y}

^{2}pairing. Thus, the fourfold symmetry in Figure 3b is not inconsistent with the H

_{c2}anisotropy originating from the d

_{x}

^{2}

_{−y}

^{2}pairing state. However, detailed magnetoresistance studies at 1.5 and 4.2 K [39] as well as Figure 3 showed the lack of in-plane anisotropy of H

_{c2}. In addition, the cusp-like minima that appear below 7.8 K cannot be represented by a simple cos4ϕ dependence. Thus, another mechanism to describe these oscillation patterns is necessary.

_{x}

^{2}

_{−y}

^{2}pairing is assumed, ρ(ϕ) should become minima at ϕ = 0° (H // c) and ϕ = 90° (H // b) and maximum at ϕ = 45°, which agrees with Figure 4b. Thus, we consider that our result concerned with flux-flow resistance is consistent with d

_{x}

^{2}

_{−y}

^{2}pairing state, as suggested by STM [13] and thermal conductivity experiments [14].

_{5}[48]. A similar problem between the thermal conductivity and heat capacity measurements was discussed for k-(ET)

_{2}Cu(NCS)

_{2}[14,15]. According to the T–H diagrams in [46,47], field-angle dependences of heat capacity and thermal conductivity do not show sign reversal pattern at H/H

_{c2}~ 0.43 and T/T

_{c}> 0.48, where our experimental study was done. Although our results are not inconsistent with no sign reversal oscillation for a wide temperature region, further experimental study such as confirmation of sign reversal pattern at lower fields will be needed to elucidate the effect of the Doppler shifted state on the vortex dynamics.

#### 3.2. β″-(ET)_{2}SF_{5}CH_{2}CF_{2}SO_{3}

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}(T

_{c}= 5.2 K) has triclinic symmetry and the ET donor molecules form 2D conduction layers parallel to the a-b plane [49]. The insulating SF

_{5}CH

_{2}CF

_{2}SO

_{3}

^{−}layer is intercalated between the ET donor layers, which makes the c*-axis the least conducting direction. Both a 2D Fermi pocket and a pair of quasi-1D Fermi sheets is predicted from the band-structure calculation [50]. The SdH effect and AMRO (angular-dependent magnetoresistance oscillation) studies clearly show one small 2D FS with an area of 5% of the first Brillouin zone [50,51]. Reflecting the layered structure, its GL coherence length perpendicular to the conducting layers, ξ

_{⊥}(0) (~ 7.9 ± 1.5 Å), is shorter than the interlayer spacing d of 17.5 Å [28].

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}. First, high field AMRO showed the nature of incoherent interlayer transport. This means that the FS of β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}is regarded as the highly 2D confined electron system [52]. Second, the FS structure is very similar to that of k-(ET)

_{2}Cu(NCS)

_{2}[49]. Third and most importantly, the SC state of β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}may be mediated by charge fluctuations because a pressure-induced charge ordering state is observed at around 1 GPa [53]. For β″ type organic conductors, a large intersite Coulomb repulsion has been theoretically predicted [6,8,54]. Moreover, d-wave superconductivity mediated by charge fluctuations has been proposed based on above theoretical study [8,55], but not confirmed experimentally. In this section, we discuss the relationship between in-plane angular variation of H

_{c2}and vortex dynamics in β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}.

#### 3.2.1. Anisotropy of Upper Critical Field in β″-(ET)_{2}SF_{5}CH_{2}CF_{2}SO_{3}

_{c2}(ϕ), within the conducting a-b plane, the interlayer resistance as a function of magnetic field at various fixed ϕ was investigated as shown by Figure 5a. The resistance curves were taken in intervals of ∆ϕ = 10°. At around the SC transition, the resistance gradually reaches zero with decreasing magnetic field. Figure 5b presents the in-plane angular variation of H

_{c2}. We define H

_{c2}, when R/R

_{n}= 0.9, 0.7, and 0.5, where R

_{n}is the normal state resistance given by extrapolating R(H) in the higher field region of 13 ≦ μ

_{0}H ≦ 14 T. It is clear that the angular variation of H

_{c2}exhibits maxima at around ϕ = ±90° and ϕ = 0°. Although the values of H

_{c2}are changed by the different criteria, the fourfold oscillation pattern of H

_{c2}itself remains.

_{c2}(ϕ) minima occur for applied field parallel to the nodal directions. Thus, it is considered that the SC gap possesses its node (or minimum) at approximately π/4 from the b-axis. This result is in favor of a d

_{x}

^{2}

_{−y}

^{2}gap symmetry [38].

#### 3.2.2. In-Plane Anisotropy of Vortex Dynamics in β″-(ET)_{2}SF_{5}CH_{2}CF_{2}SO_{3}

_{c2}, the in-plane anisotropy of the vortex dynamics is next shown. Figure 6 presents the polar angle dependence of the interlayer resistance at various ϕ values. The structures around θ = 90° (i.e., dip or peak) depend on ϕ, showing the anisotropic vortex dynamics within the conducting layers. To see the anisotropic field effect, the ϕ-dependence of the interlayer resistance at θ = 90° for various currents is shown in Figure 7a. At 100 μA, we observe a fourfold angular oscillation: cusp-like minima are observed at ϕ = 20° and ±90°. With increasing current, the amplitude increases, showing the remarkable non-ohmic transport phenomena. Figure 7b presents ϕ-dependence of the interlayer resistance at θ = 90° for several magnetic fields. As shown by Figure 7b, the effect of magnetic field on the flux-flow resistance is very similar to Figure 7a. With increasing magnetic field, a non-sinusoidal fourfold angular pattern is found. The cusp-like minima are observed at ϕ = 20° and ±90° that are the same as Figure 7a. The current dependence of the flux-flow resistance at a fixed field strength (Figure 7a) is very similar to the field dependence of that at a fixed current (Figure 7b), suggesting that combination of high magnetic field and large current, that is, Lorentz force plays an important role for appearance of the fourfold pattern in the flux-flow resistance. Similar fourfold pattern has been found in the flux-flow resistance in k-(ET)

_{2}Cu(NCS)

_{2}[25].

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, when d

_{x}

^{2}

_{−y}

^{2}pairing, as discussed in Figure 4b, is assumed, R(ϕ) should have minima at around ϕ = ±90° and ϕ = 0° and it should have maxima at around ϕ = ±45° orientations, and therefore this is consistent with Figure 7a,b.

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}. The nodal orientations discussed here are far from the orientations of most effective nesting vector on the Fermi surface predicted from the band-structure calculation, as well as determined from the AMRO experiments [26,50,51]. If a spin fluctuation scenario is assumed, it is natural to expect the nodes that are parallel to the antiferromagnetic nesting vector, to be along the b* and a* (or a) orientations. It is intriguing to point out that superconductivity with another d-wave symmetry is theoretically suggested based on the charge fluctuation scenario [55]. Further investigation is needed to elucidate which mechanism (i.e., spin fluctuations versus charge fluctuations) is more likely.

#### 3.3. λ-(BETS)_{2}GaCl_{4}

_{2}GaCl

_{4}undergoes a SC transition at T

_{c}of ~8 K [56]. The BETS donor molecules are stacked along the a- and c-axes. The insulating GaCl

_{4}

^{−}anion layers are inserted between the BETS conducting layers. Thus, the 2D conducting layers are formed in λ-(BETS)

_{2}GaCl

_{4}. Reflecting the layered structure, its GL coherence length perpendicular to the layers is shorter than the interlayer spacing of 18.6 Å [57]. λ-(BETS)

_{2}GaCl

_{4}is known as a good candidate for realizing the Fulde–Ferrell–Larkin–Ovchinnikov state [57,58]. Another intriguing point is that its isostructural compound λ-(BETS)

_{2}FeCl

_{4}shows a field-induced SC transition [59]. Band-structure calculation [56] predicts the existence of one closed 2D Fermi pocket and two 1D Fermi sheets that are topologically the same as k-(ET)

_{2}Cu(NCS)

_{2}[50,51]. Measurements of the SdH and AMROs are qualitatively consistent with the band calculation [60].

_{xy}–wave symmetry with the line nodes along the a*- and c*-axes [61]. From systematic investigations by chemical substitution in the anions [62,63] or by selecting different donor molecules [64], the SC phase is suggested to exist next to the Mott insulating phase, which is similar to the k-(ET)

_{2}X system [65]. An NMR study showed the development of spin fluctuations beyond the SC phase transition temperature [66]. A heat capacity study showed a d-wave pairing state [67], whereas a μSR study clamed a mixture of the extended s- and d-wave SC gap [68]. In this section, we discuss the interplay between in-plane anisotropy of vortex dynamics and the SC gap structure for λ-(BETS)

_{2}GaCl

_{4}[26].

#### In-Plane Anisotropy of Vortex Dynamics in λ-(BETS)_{2}GaCl_{4}

_{2}Cu(NCS)

_{2}[25] and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}[27] even though the FS geometry of λ-(BETS)

_{2}GaCl

_{4}[56] is similar to that of k-(ET)

_{2}Cu(NCS)

_{2}[60] and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}[50,51].

_{2}GaCl

_{4}while fourfold-symmetric flux-flow resistance for β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}and k-(ET)

_{2}Cu(NCS)

_{2}. As a possible explanation, we consider that the different anisotropic feature may be related to the difference of the interlayer coupling strength [31]. The anisotropy parameter Γ, given by (ξ

_{//}/ξ

_{⊥})

^{2}, for β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}is Γ ~ 330 that is larger the those of k-(ET)

_{2}Cu(NCS)

_{2}(Γ ~ 100) and λ-(BETS)

_{2}GaCl

_{4}(Γ ~ 60) [27]. Since λ-(BETS)

_{2}GaCl

_{4}is more three dimensional than k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, an orbital pair breaking effect in λ-(BETS)

_{2}GaCl

_{4}is stronger than in k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}.

_{2}GaCl

_{4}, the superposition of the normal-state magnetoresistance cannot be avoided in the in-plane anisotropy of the flux-flow resistance. Figure 10 presents the in-plane angular dependence of normal-state magnetoresistance in the magnetic field of 14.8 T [26]. The normal-state magnetoresistance possesses the twofold symmetry with broad maximum at around ϕ = −20°. The result is consistent with Tanatar et al. [57]. The twofold symmetric normal-state magnetoresistance can be understood in terms of Fermi-surface anisotropy if it mainly originates from the ellipsoidal 2D pocket elongated along the c-axis. In the small Γ system, the large twofold component in the normal-state magnetoresistance may mask the fourfold ones.

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}. The origin of the dip in λ-(BETS)

_{2}GaCl

_{4}should be the same as that in k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}. To theoretically discuss the SC gap structure for λ-(BETS)

_{2}GaCl

_{4}, Aizawa et al. [69] performed first-principles band calculation. Considering the spin-fluctuation-mediated mechanism, they discussed the SC gap function by applying the random phase approximation. They showed that the obtained SC gap changes its sign four times along the Fermi surface, suggesting a d-wave SC gap in λ-(BETS)

_{2}GaCl

_{4}. Reflecting the low symmetry of the crystal structure in λ-(BETS)

_{2}GaCl

_{4}, however, the SC gap has only twofold symmetry. It means that the predicted SC gap has a large gap between narrow opening nodes with an acute angle (around the steep node structure) and a small gap between wide opening nodes with an obtuse angle. Recent magnetic-field-angle-resolved heat capacity study [70] is consistent with theoretically predicted SC gap function. The large gap is located along the c-axis [69] which agrees with the position of sharp dip [26]. The small gap exists at around a-axis [69], where we observed broad minimum in flux-flow resistance [26]. Thus, experimental results of flux-flow resistance in λ-(BETS)

_{2}GaCl

_{4}[26] are consistent with the d-wave gap structure theoretically discussed by Aizawa [69].

## 4. Summary

_{2}Cu(NCS)

_{2}, β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, and λ-(BETS)

_{2}GaCl

_{4}. We observed clear fourfold-symmetric anisotropy in the interlayer flux-flow resistance for k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, while only twofold symmetry in λ-(BETS)

_{2}GaCl

_{4}. For k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}, flux-flow resistivity showing fourfold oscillation can be consistently explained by assuming the enhanced viscous motion of vortices by QPs arising from the Doppler effect. Absence of the fourfold anisotropy in λ-(BETS)

_{2}GaCl

_{4}is discussed in the two regimes. The first regime is related to the stronger interlayer coupling in the λ-(BETS)

_{2}GaCl

_{4}system as compared with k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}. The second regime is discussed in terms of recent theoretical study by Aizawa et al. In this scenario, flux-flow resistivity with twofold anisotropy may be associated with the crystal structure with low symmetry, which is rather different from those of k-(ET)

_{2}Cu(NCS)

_{2}and β″-(ET)

_{2}SF

_{5}CH

_{2}CF

_{2}SO

_{3}.

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) (Upper left side) Schematic structure of donor conducting layers and anion insulating layers in a layered organic conductor. (Upper right side) Structures of ET and BETS donor molecules. (Lower side) Three patterns within packed donor conducting layers for (

**b**) k-, (

**c**) β″-, and (

**d**) λ-type arrangements.

**Figure 3.**(

**a**) Temperature dependence of interlayer resistance for various magnetic fields H // b (ϕ = 90°) in κ-(ET)

_{2}Cu(NCS)

_{2}. (

**b**) H–T phase diagram derived from (

**a**), where four criteria, J (junction), M (midpoint), X (R → 0), and Z (R = 0) are plotted for T

_{c}(H).

**Figure 4.**(

**a**) Polar angle dependence of interlayer resistance at 5.0 K under a magnetic field of 13 T for various values of ϕ. The curves are measured in intervals of ∆ϕ = 5° between 120° (top curve) and −20° (bottom). (

**b**) Dependence of resistivity at θ = 90° at various temperatures. (Reprinted from [25]. Copyright 2013 The Physical Society of Japan.)

**Figure 5.**(

**a**) Magnetic field dependence of interlayer resistance at various fixed ϕ in the ohmic regime, where applied field is parallel to the conducting plane. The curves are taken from ϕ = 100° (top curve) to −100° (bottom) with intervals of Δϕ = 10°. (

**b**) In-plane angular variation of H

_{c2}determined from the resistive transition. The H

_{c2}values are defined as the fields at which the resistance of the measured sample has reached 90%, 70%, and 50% of its normal-state value. (Reprinted from [27]. Copyright 2015 The Physical Society of Japan.)

**Figure 6.**Polar angle dependence of interlayer resistance for various fixed ϕ values. The curves are taken in intervals of ∆ϕ = 10° between ϕ = 100° (top curve) and −100° (bottom). (Reprinted from [27]. Copyright 2015 The Physical Society of Japan.).

**Figure 7.**Azimuth angle dependence of the flux-flow resistance for several values of current (

**a**) and of magnetic field (

**b**). (Reprinted from [27]. Copyright 2015 The Physical Society of Japan.)

**Figure 8.**Polar angle dependence of interlayer resistance under rotating field of 8.5 T for various fixed ϕ. The curves are taken in intervals of ∆ϕ = 10° between −80° (top curve) and 120° (bottom). (Reprinted from [26]. Copyright 2014 The Physical Society of Japan.)

**Figure 9.**Azimuth angle dependence of flux-flow resistance in λ−(BETS)

_{2}GaCl

_{4}at various currents. A sharp minimum is observed at ϕ = 0° (H // c). (Reprinted from [26]. Copyright 2014 The Physical Society of Japan.)

**Figure 10.**Azimuth angle dependence of normal-state magnetoresistance in λ−(BETS)

_{2}GaCl

_{4}within the conducting plane. (Reprinted from [26]. Copyright 2014 The Physical Society of Japan.)

Properties | Unit | κ-(ET)_{2}Cu(NCS)_{2} | β”-(ET)_{2}SF_{5}CH_{2}CF_{2}SO_{3} | λ-(BETS)_{2}GaCl_{4} |
---|---|---|---|---|

T_{c} | K | 8.7–10.4 | 5.2 | 5–8 |

B_{c1‖} | mT | 0.2 | 0.006 | 5.2 |

B_{c1⊥} | mT | 6.5 | 2 | 8.2 |

B_{c2‖} | T | 30–35 | 10.4 | 12 |

B_{c2⊥} | T | 6 | 1.4 | 3 |

λ_{‖} | Å | 5100–20,000 | 10,000–20,000 | 1500 |

λ_{⊥} | μm | 40–200 | 400–800 | |

ξ_{‖} | Å | 74 | 144 | 105 |

ξ_{⊥} | Å | 5–9 | 7.9 | 9–14 |

κ_{‖} | - | 100–200 | 59 | 107 |

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Yasuzuka, S. Interplay between Vortex Dynamics and Superconducting Gap Structure in Layered Organic Superconductors. *Crystals* **2021**, *11*, 600.
https://doi.org/10.3390/cryst11060600

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Yasuzuka S. Interplay between Vortex Dynamics and Superconducting Gap Structure in Layered Organic Superconductors. *Crystals*. 2021; 11(6):600.
https://doi.org/10.3390/cryst11060600

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Yasuzuka, Syuma. 2021. "Interplay between Vortex Dynamics and Superconducting Gap Structure in Layered Organic Superconductors" *Crystals* 11, no. 6: 600.
https://doi.org/10.3390/cryst11060600