We present magnetic-torque experiments on the organic superconductor k-(BEDT-TTF)2Cu(NCS)2 for magnetic fields applied parallel to the 2D superconducting layers. The experiments show a crossover from a second-order to a first-order transition when the upper critical field reaches 21 T. Beyond this field, which we interpret as the Pauli limit for superconductivity, the upper critical field line shows a pro-nounced upturn and a phase transition line separates the superconducting state into a low- and a high-field phase. We interpret the data in the framework of a Fulde-Ferrell-Larkin-Ovchinnikov state.
We report measurements of the de Haas-van Alphen (DHVA) effect and AC susceptibility in the layered organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The amplitude of the DHVA oscillations is attenuated over a wide field range above the irreversibility line, B_irr(B), below which a rigid flux lattice is formed. Thus the DHVA effect provides a unique probe of the superconducting fluctuations at high fields in this material. We compare our measurements with other determinations of the superconducting phase diagram of $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$.
The specific heat of the layered organic superconductor $κ$-% (BEDT-TTF)$_2$Cu(NCS)$_2$, where BEDT-TTF is bisethylenedithio-% tetrathiafulvalene, has been studied in magnetic fields up to 28 T applied perpendicular and parallel to the superconducting layers. In parallel fields above 21 T, the superconducting transition becomes first order, which signals that the Pauli-limiting field is reached. Instead of saturating at this field value, the upper critical field increases sharply and a second first-order transition line appears within the superconducting phase. Our results give strong evidence…
The thermal conductivity of organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2 (Tc =10.4 K) has been studied in a magnetic field rotating within the 2D superconducting planes with high alignment precision. At low temperatures (T < 0.5 K), a clear fourfold symmetry in the angular variation, which is characteristic of a d-wave superconducting gap with nodes along the directions rotated 45 degrees relative to the b and c axes of the crystal, was resolved. The determined nodal structure is inconsistent with recent theoretical predictions of superconductivity induced by the antiferromagnetic spin flu…
The vortex state in a single crystal of the layered organic superconductor κ-(BEDT-TTF2Cu(NCS)2, where BEDT-TTF (or ET) is bis(ethylenedithio)tetrathiafulvalene, was studied by 1H-NMR. Under a low field region around 0.75 T, the vortex glass-liquid transition was demonstrated by a diverging of the longitudinal nuclear spin relaxation rate and peak-broadening in spectra. Under a high field region near the upper critical field Hc2(0)~7 T, the curvature of nuclear spin relaxation curves showed a drastic change at the temperature where the emergence of the quantum vortex slush state was reported. …
We have studied the interlayer resistivity of the prototypical quasi-two-dimensional organic superconductor $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ as a function of temperature, current and magnetic field, within the superconducting state. We find a region of non-zero resistivity whose properties are strongly dependent on magnetic field and current density. There is a crossover to non-Ohmic conduction below a temperature that coincides with the 2D vortex solid -- vortex liquid transition. We interpret the behaviour in terms of a model of current- and thermally-driven phase slips caused by the diffusive …
Details of the Fermi-surface topology of deuterated $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ ~have been measured as a function of pressure, and compared with equivalent measurements of the undeuterated salt. We find that the superconducting transition temperature is much more dramatically suppressed by increasing pressure in the deuterated salt. It is suggested that this is linked to pressure-induced changes in the Fermi-surface topology, which occur more rapidly in the deuterated salt than in the undeuterated salt as the pressure is raised. Our data suggest that the negative isotope effect observed on d…
Single crystals of the layered organic type II superconductor, $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$, have been studied in magnetic fields of up to 33 T and at temperatures between 0.5 K and 11 K using a compact differential susceptometer. When the magnetic field lies precisely in the quasi-two-dimensional planes of the material, there is strong evidence for a phase transition from the superconducting mixed state into a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, manisfested as a change in the rigidity of the vortex system. The behaviour of the transition as a function of temperature is in good…
We present magnetic-torque measurements of the organic superconductor k-(BEDT-TTF)2Cu(NCS)2 for in-plane magnetic fields up to 32 T. In this layered two-dimensional compound the superconductivity can persist even in fields above the Pauli limit of about 21 T. There, a pronounced upturn of the upper-critical-field line occurs and the superconducting phase-transition line splits and forms an additional high magnetic field phase. k-(BEDT-TTF)2Cu(NCS)2 is a spin-singlet superconductor, therefore, such a superconducting high-field phase beyond the Pauli limit can originate only from Cooper pairing …
The suppression of superconductivity by nonmagnetic disorder is investigated systematically in the organic superconductor $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$. We introduce a nonmagnetic disorder arising from molecule substitution in part with deuterated BEDT-TTF or BMDT-TTF for BEDT-TTF molecules and molecular defects introduced by X-ray irradiation. A quantitative evaluation of the scattering time $τ_{\rm dHvA}$ is carried out by de Haas-van Alphen (dHvA) effect measurement. A large reduction in $T_{\rm c}$ with a linear dependence on $1/τ_{\rm dHvA}$ is found in the small-disorder region below $1/…
Angle and temperature dependent torque magnetization measurements are reported for the organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2, at extremely low temperatures (approx. Tc/10^3). Magneto-thermal instabilities are observed in the form of abrupt magnetization (flux) jumps. We carry out an analysis of the temperature and field orientation dependence of these flux jumps based on accepted models for layered type-II superconductors. Using a simple Bean model, we also find a critical current density of 4x10^8 A/m^2 from the remnant magnetization, in agreement with previous measurements.
The first study of thermal conductivity, $κ$, in a quasi-two-dimensional organic superconductor of the $κ$-(BEDT-TTF)$_2$X family reveals features analogous to those already observed in the cuprates. The onset of superconductivity is associated with a sudden increase in $κ$ which can be suppressed by the application of a moderate magnetic field. At low temperatures, a finite linear term - due to a residual electronic contribution- was resolved. The magnitude of this term is close to what is predicted by the theory of transport in unconventional superconductors.
We performed $^{13}$C-NMR experiment and measured spin-lattice relaxation rate divided by temperature $1/T_{1}T$ near the superconducting (SC) transition temperature $T_{c}$ in $κ$-(BEDT-TTF)$_{2}$Cu[N(CN)$_{2}$]Br ($κ$-Br salt), and $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$ ($κ$-NCS salt). We observed the reduction of $1/T_{1}T$ starting at the temperature higher than $T_c$ in $κ$-Br salt. Microscopic observation of quasi-particle density of states in the fluctuating SC state revealed the effects of short-range Cooper pairs induced in the normal state to the quasi-particle density of states. We also …
We report the transport properties in the vortex liquid states induced by quantum fluctuations at low temperature in the layered organic superconductor kappa-(BEDT-TTF)_{2} Cu(NCS)_{2}. A steep drop of the resistivity observed below about 1 K separates the liquid state into two regions. In the low resistance state at lower temperature, a finite resistivity with weak temperature dependence persists down to 100 mK at least. The finite resistivity in the vortex state at T ~= 0 K indicates the realization of quantum vortex liquid assisted by the strong quantum fluctuations instead of the thermal o…
We report high-resolution specific heat measurements on the quasi-2D organic superconductor $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$, performed by using a most sensitive ac-modulation technique. The main observations are (i) a discontinuity at \tc\ much in excess of what is expected for a weak-coupling BCS superconductor and (ii) a quasiparticle contribution to the specific heat with an exponentially weak temperature dependence at $T \ll T_c$. The latter finding is incompatible with an order parameter that vanishes at certain parts of the Fermi surface. The data for $T \leq T_c$ can be well described by …
We compare the theoretical anisotropic upper critical field $H_{C}(Θ,T)$ of a quasi-two-dimensional d-wave superconductor with recent $H_{c2}$ data for the layered organic superconductor $κ-(BEDT-TTF)_2Cu(NCS)_2$. We find agreement both with regard to the angular and the temperature dependence of $H_{C}$. This supports the suggestion that the Fulde-Ferrell-Larkin-Ovchinnikov state (FFLO state) exists in this material for exactly plane-parallel orientation of the magnetic field. Indications of precursor states, occurring for small deviations from the plane-parallel field direction, are also poi…
We report the Shubnikov-de Haas (SdH) oscillations observed in the vortex liquid state of the quasi two dimensional organic superconductor $κ$-(BEDT-TTF)$_{2}$Cu(NCS)$_{2}$. The SdH oscillations can be observed down to about 5 T at 0.5 K, where the flux flow resistivity becomes as small as about 30 % of the normal state value. Below the upper critical field $H_{\rm c2}$ of about 7 T, the additional damping of the SdH oscillation amplitude appears, as well as that of the de Haas-van Alphen (dHvA) oscillations, with respect to the normal state one which is described with the standard Lifshitz-Ko…
We report the in-plane penetration depth $λ_{\parallel}$ of single crystals $κ$-(BEDT-TTF)$_2X$ ($X=$ Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br) by means of the reversible magnetization measurements under the control of cooling-rate. In $X$ = Cu(NCS)$_2$, $λ_{\parallel}(0)$ as an extrapolation toward $T$ = 0 K does not change by the cooling-rate within the experimental accuracy, while $T_{\textrm{c}}$ is slightly reduced. On the other hand, in $X$ = Cu[N(CN)$_2$]Br, $λ_{\parallel}(0)$ indicates a distinct increase by cooling faster. The different behavior of $λ_{\parallel}(0)$ on cooling-rate between th…
A cavity perturbation technique is used to study the microwave response of the organic superconductor k-(BEDT-TTF)2Cu(NCS)2. Observation of a Josephson plasma resonance, below Tc (approx. 10 K), enables investigation of the vortex structure within the mixed state of this highly anisotropic, type-II, superconductor. Contrary to previous assumptions, frequency dependent studies (28 - 153 GHz) indicate that the squared plasma frequency depends exponentially on the magnetic field strength. Such behavior has been predicted for a weakly pinned quasi-two-dimensional vortex lattice [Bulaevskii et al. …
Using a high-sensitivity cavity perturbation technique (40 to 180 GHz), we have probed the angle dependent interlayer magneto-electrodynamic response within the vortex state of the extreme two-dimensional organic superconductor k-(BEDT-TTF)2Cu(NCS)2. A previously reported Josephson plasma resonance [M. Mola et al., Phys. Rev. B 62, 5965 (2000)] exhibits a dramatic re-entrant behavior for fields very close (<1 degree) to alignment with the layers. In this same narrow angle range, a new resonant mode develops which appears to be associated with the non-equilibrium critical state. Fits to the ang…
A microwave cavity perturbation technique is used to probe the interlayer electrodynamics within the vortex state of the organic superconductor kappa-(BEDT-TTF)2Cu(NCS)2. A Josephson plasma mode is observed which is extremely sensitive to correlations in the locations of vortices in adjacent layers and may, therefore, be used to gauge collective effects between vortices and crystal pinning sites in the title compound. Our previous investigations [M. M. Mola et al., Phys. Rev. B 62 (2000) 5965] revealed a transformation from a correlated quasi-two-dimensional pinned vortex phase, to either a de…
The magnetic susceptibility of the organic superconductors $κ$-(h8 or d8-ET)$_{2}$$X$, $X =$ Cu(NCS)$_{2}$ and Cu[N(CN)$_{2}$]Br has been studied. A metallic phase below $T^{*} =$ 37 $\sim$ 38 K for $X =$ Cu[N(CN)$_{2}$]Br and 46 $\sim$ 50 K for $X =$ Cu(NCS)$_{2}$ has an anisotropic temperature dependence of the susceptibility and the charge transport. Partial charge-density-wave or charge fluctuation is expected to coexist with the metallic phase instead of the large antiferromagnetic fluctuation above $T^{*}$. The phase diagram and the superconductivity of $κ$-(ET)$_{2}$$X$ are discussed in…
We present upper critical field data for $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ with the magnetic field close to parallel and parallel to the conducting layers. We show that we can eliminate the effect of vortex dynamics in these layered materials if the layers are oriented within 0.3 degrees of parallel to the applied magnetic field. Eliminating vortex effects leaves one remaining feature in the data that corresponds to the Pauli paramagnetic limit ($H_p$). We propose a semi-empirical method to calculate the $H_p$ in quasi 2D superconductors. This method takes into account the energy gap of each of th…
Superconductivity is a quantum phenomena arising, in its simplest form, from pairing of fermions with opposite spin into a state with zero net momentum. Whether superconductivity can occur in fermionic systems with unequal number of two species distinguished by spin, atomic hyperfine states, flavor, presents an important open question in condensed matter, cold atoms, and quantum chromodynamics, physics. In the former case the imbalance between spin-up and spin-down electrons forming the Cooper pairs is indyced by the magnetic field. Nearly fifty years ago Fulde, Ferrell, Larkin and Ovchinnikov…
We present high-resolution measurements of the coefficient of thermal expansion $α(T)=\partial \ln l(T)/\partial T$ of the quasi-twodimensional (quasi-2D) salts $κ$-(BEDT-TTF)$_2$X with X = Cu(NCS)$_2$, Cu[N(CN)$_2$]Br and Cu[N(CN)$_2$]Cl. At intermediate temperatures (B), distinct anomalies reminiscent of second-order phase transitions have been found at $T^\ast = 38$ K and 45 K for the superconducting X = Cu(NCS)$_2$ and Cu[N(CN)$_2$]Br salts, respectively. Most interestingly, we find that the signs of the uniaxial pressure coefficients of $T^\ast$ are strictly anticorrelated with those of $…
Peaks in the magnetoresistivity of the layered superconductor $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$, measured in fields $\leq 45$ T applied within the layers, show that the Fermi surface is extended in the interlayer direction and enable the interlayer transfer integral ($t_{\perp} \approx 0.04$ meV) to be deduced. However, the quasiparticle scattering rate $τ^{-1}$ is such that $\hbar/τ\sim 6t_{\perp}$, implying that $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ meets the criterion used to identify interlayer incoherence. The applicability of this criterion to anisotropic materials is thus shown to be questionable.
Resonant optical excitation of certain molecular vibrations in $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br has been shown to induce transient superconducting-like optical properties at temperatures far above equilibrium $T_c$. Here, we report experiments across the bandwidth-tuned phase diagram of this class of materials, and study the Mott insulator $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Cl and the metallic compound $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$. We find non-equilibrium photoinduced superconductivity only in $κ$-(BEDT-TTF)$_2$Cu[N(CN)$_2$]Br, indicating that the proximity to the Mott insulating phase and possi…
Unconventional density waves (UDW) are one of the ground states in metallic crystalline solids and have been speculated already in 1968. However, more focused studies on UDW started only recently, perhaps after the identification of the low temperature phase in alpha-(BEDT-TTF)_2KHg(SCN)_4 as unconventional charge density wave (UCDW) in 2002. More recently, the metallic phase of Bechgaard salts (TMTSF)_2X with X=PF_6 and ReO_4 under both pressure and magnetic field appears to be unconventional spin density wave (USDW). The pseudogap regime of high T_c superconductors LSCO, YBCO, Bi2212 and the…
We theoretically study the orbital destructive effect against superconductivity in a parallel magnetic field in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO or LOFF) phase at zero temperature in a quasi-two-dimensional (Q2D) conductor. We demonstrate that at zero temperature a special parameter, $λ= l_{\perp}(H)/d$, is responsible for strength of the orbital effect, where $l_{\perp}(H)$ is a typical "size" of the quasi-classical electron orbit in a magnetic field and $d$ is the inter-plane distance. We discuss applications of our results to the existing experiments on the FFLO phase in the organ…
Nuclear magnetic resonance measurements were performed on CeCu$_{2}$Si$_{2}$ in the presence of a magnetic field close to the upper critical field $μ_{0} H_{\rm c2}$ in order to investigate its superconducting (SC) properties near pair-breaking fields. In lower fields, the Knight shift and nuclear spin-lattice relaxation rate divided by temperature $1/T_1T$ abruptly decreased below the SC transition temperature $T_{\rm c}(H)$, a phenomenon understood within the framework of conventional spin-singlet superconductivity. In contrast, $1/T_1T$ was enhanced just below $T_{\rm c}(H)$ and exhibited a…
We show that there are strong similarities in the spin lattice relaxation of non-magnetic organic charge transfer salts, and that these similarities can be understood in terms of spin fluctuations. Further, we show that, in all of the kappa-phase organic superconductors for which there is nuclear magnetic resonance data, the energy scale for the spin fluctuations coincides with the energy scale for the pseudogap. This suggests that the pseudogap is caused by short-range spin correlations. In the weakly frustrated metals k-(BEDT-TTF)_2Cu[N(CN)_2]Br, k-(BEDT-TTF)_2Cu(NCS)_2, and k-(BEDT-TTF)_2Cu…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can emerge in superconductors for which the orbital critical field exceeds the Pauli limit. Here, we present angular-resolved specific-heat data of the quasi-two-dimensional organic superconductor $κ$-(ET)$_2$Cu(NCS)$_2$, with a focus on high fields in the regime of the FFLO transition. For an increasing out-of-plane tilt of the applied magnetic field, which leads to an increase of orbital contributions, we found that the nature of the superconducting transition changes from second to first order and that a further transition appears within the…
We present a group theoretic analysis of several classes of organic superconductors. We argue that highly frustrated half-filled layered organic superconductors, such as kappa-(ET)_2Cu2(CN)_3 (where ET is BEDT-TTF) and beta'-[Pd(dmit)_2]_2X, undergo two superconducting phase transitions, the first from the normal state to a d-wave superconductor and the second to a d+id state. We show that the monoclinic distortion of kappa-(ET)_2Cu(NCS)_2 means that the symmetry of its superconducting order parameter is different from that of orthorhombic kappa-(ET)_2Cu[N(CN)_2]Br. We propose that quarter fil…
We have recently reported the first direct calorimetric observation of a magnetic-field-induced first-order phase transition into a high-field FFLO superconducting state at the Clogston-Chandrasekar `Pauli' paramagnetic limit $H_p$ in a 2D superconductor $κ-{\textrm{(BEDT-TTF)}}_2{\textrm{Cu}}{\textrm{(NCS)}}_2$. The high-field state is both higher entropy and strongly paramagnetic, as thermodynamically required for the FFLO state. Here we compare our results with theoretical predictions for the field dependence of the high-field FFLO state in the 2D limit, revealing tentative evidence for tra…
We present a microscopic approach to the calculations of thermal conductivity in unconventional superconductors for a wide range of temperatures and magnetic fields. Our work employs the non-equilibrium Keldysh formulation of the quasiclassical theory. We solve the transport equations using a variation of the Brandt-Pesch-Tewordt (BPT) method, that accounts for the quasiparticle scattering on vortices. We focus on the dependence of the thermal conductivity on the direction of the field with the respect to the nodes of the order parameter, and discuss it in the context of experiments aiming to …
Although quasi-two-dimensional organic superconductors such as $κ$-(BEDT-TTF)$_2$Cu(NCS)$_2$ seem to be very clean systems, with apparent quasiparticle mean-free paths of several thousand Å, the superconducting transition is intrinsically broad (e.g $\sim 1$ K wide for $T_c \approx 10$ K). We propose that this is due to the extreme anisotropy of these materials, which greatly exacerbates the statistical effects of spatial variations in the potential experienced by the quasiparticles. Using a statistical model, we are able to account for the experimental observations. A parameter $\bar{x}$, whi…
We report the first magneto-caloric and calorimetric observations of a magnetic-field-induced phase transition within a superconducting state to the long-sought exotic "FFLO" superconducting state first predicted over 50 years ago. Through the combination of bulk thermodynamic calorimetric and magnetocaloric measurements in the organic superconductor $κ$ - (BEDT-TTF)$_2$Cu(NCS)$_2$, as a function of temperature, magnetic field strength, and magnetic field orientation, we establish for the first time that this field-induced first-order phase transition at the paramagnetic limit $H_p$ for tradit…
After a brief introduction to crystalline organic superconductors and metals, we shall describe two recently-observed exotic phases that occur only in high magnetic fields. The first involves measurements of the non-linear electrical resistance of single crystals of the charge-density-wave (CDW) system (Per)$_2$Au(mnt)$_2$ in static magnetic fields of up to 45 T and temperatures as low as 25 mK. The presence of a fully gapped CDW state with typical CDW electrodynamics at fields higher that the Pauli paramagnetic limit of 34 T suggests the existence of a modulated CDW phase analogous to the Ful…
