Microscopic Study of the Fulde-Ferrell-Larkin-Ovchinnikov State in an All-Organic Superconductor

Exotic Superfluid Phases in Spin-Polarized Fermi Gases in Optical Lattices

Leveraging cutting-edge numerical methodologies, we study the ground state of the two-dimensional spin-polarized Fermi gas in an optical lattice. We focus on systems at high density and small spin polarization, corresponding to the parameter regime believed to be most favorable to the formation of the elusive Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. Our systematic study of large lattice sizes, hosting nearly 500 atoms, provides strong evidence of the stability of the FFLO state in this regime, as well as a high-accuracy characterization of its properties. Our results for the density correlation function reveal the existence of density order in the system, suggesting the possibility of an intricate coexistence of long-range orders in the ground state. The ground-state properties are seen to differ significantly from the standard mean-field description, providing a compelling avenue for future theoretical and experimental explorations of the interplay between spin imbalance, strong interactions, and superfluidity in an exotic phase of matter.

Superconducting spin smecticity evidencing the Fulde-Ferrell-Larkin-Ovchinnikov state in Sr2RuO4

Translational symmetry breaking is antagonistic to static fluidity but can be realized in superconductors, which host a quantum-mechanical coherent fluid formed by electron pairs. A peculiar example of such a state is the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, induced by a time-reversal symmetry-breaking magnetic field applied to spin-singlet superconductors. This state is intrinsically accompanied by the superconducting spin smecticity, spin density-modulated fluidity with spontaneous translational-symmetry breaking. Detection of such spin smecticity provides unambiguous evidence for the FFLO state, but its observation has been challenging. Here, we report the characteristic "double-horn" nuclear magnetic resonance spectrum in the layered superconductor Sr₂RuO₄ near its upper critical field, indicating the spatial sinusoidal modulation of spin density that is consistent with superconducting spin smecticity. Our work reveals that Sr₂RuO₄ provides a versatile platform for studying FFLO physics.

Topological Doping and Superconductivity in Cuprates: An Experimental Perspective

Hole doping into a correlated antiferromagnet leads to topological stripe correlations, involving charge stripes that separate antiferromagnetic spin stripes of opposite phases. The topological spin stripe order causes the spin degrees of freedom within the charge stripes to feel a geometric frustration with their environment. In the case of cuprates, where the charge stripes have the character of a hole-doped two-leg spin ladder, with corresponding pairing correlations, anti-phase Josephson coupling across the spin stripes can lead to a pair-density-wave order in which the broken translation symmetry of the superconducting wave function is accommodated by pairs with finite momentum. This scenario is now experimentally verified by recently reported measurements on La2−xBaxCuO4 with x=1/8. While pair-density-wave order is not common as a cuprate ground state, it provides a basis for understanding the uniform d-wave order that is more typical in superconducting cuprates.

The FFLO State in the Dimer Mott Organic Superconductor κ-(BEDT-TTF)2Cu[N(CN)2]Br

The superconducting phase diagram for a quasi-two-dimensional organic superconductor, κ-(BEDT-TTF)2Cu[N(CN)2]Br, was studied using pulsed magnetic field penetration depth measurements under rotating magnetic fields. At low temperatures, Hc2 was abruptly suppressed even by small tilts of the applied fields owing to the orbital pair-breaking effect. In magnetic fields parallel to the conducting plane, the temperature dependence of the upper critical field Hc2 exhibited an upturn and exceeded the Pauli limit field HP in the lower temperature region. Further analyses with the second derivative of the penetration depth showed an anomaly at 31–32 T, which roughly corresponded to HP. The origin of the anomaly should not be related to the orbital effect, but the paramagnetic effect, which is almost isotropic in organic salts, because it barely depends on the field angle. Based on these results, the observed anomaly is most likely due to the transition between the Bardeen-Cooper-Schrieffer (BCS) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. Additionally, we discuss the phase diagram and physical parameters of the transition by comparing them with other FFLO candidates.

Modern History of Organic Conductors: An Overview

This short review article provides the reader with a summary of the history of organic conductors. To retain a neutral and objective point of view regarding the history, background, novelty, and details of each research subject within this field, a thousand references have been cited with full titles and arranged in chronological order. Among the research conducted over ~70 years, topics from the last two decades are discussed in more detail than the rest. Unlike other papers in this issue, this review will help readers to understand the origin of each topic within the field of organic conductors and how they have evolved. Due to the advancements achieved over these 70 years, the field is nearing new horizons. As history is often a reflection of the future, this review is expected to show the future directions of this research field.

Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov state in bulk NbS2

We present measurements of the magnetic torque, specific heat and thermal expansion of the bulk transition metal dichalcogenide (TMD) superconductor NbS₂ in high magnetic fields, with its layer structure aligned strictly parallel to the field using a piezo rotary positioner. The upper critical field of superconducting TMDs in the 2D form is known to be dramatically enhanced by a special form of Ising spin orbit coupling. This Ising superconductivity is very robust to the Pauli paramagnetic effect and can therefore exist beyond the Pauli limit for superconductivity. We find that superconductivity beyond the Pauli limit still exists in bulk single crystals of NbS₂ for a precisely parallel field alignment. However, the comparison of our upper critical field transition line with numerical simulations rather points to the development of a Fulde-Ferrell-Larkin-Ovchinnikov state above the Pauli limit as a cause. This is also consistent with the observation of a magnetic field driven phase transition in the thermodynamic quantities within the superconducting state near the Pauli limit.

Superconductivity is often destroyed under magnetic field larger than a critical value called Pauli limit. Here, the authors report superconductivity beyond the Pauli limit in bulk single crystals of NbS₂, suggesting the development of a Fulde-Ferrell-Larkin-Ovchinnikov state.

Strong In-Plane Magnetic Field-Induced Reemergent Superconductivity in the van der Waals Heterointerface of NbSe2 and CrCl3

A magnetic field is generally considered to be incompatible with superconductivity as it tends to spin-polarize electrons and breaks apart the opposite-spin singlet superconducting Cooper pairs. Here, an experimental phenomenon is observed that an intriguing reemergent superconductivity evolves from a conventional superconductivity undergoing a hump-like intermediate phase with a finite electric resistance in the van der Waals heterointerface of layered NbSe₂ and CrCl₃ flakes. This phenomenon merely occurred when the applied magnetic field is parallel to the sample plane and perpendicular to the electric current direction as compared to the reference sample of a NbSe₂ thin flake. The strong anisotropy of the reemergent superconducting phase is pointed to the nature of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state driven by the strong interfacial spin-orbit coupling between NbSe₂ and CrCl₃ layers. The theoretical picture of FFLO state nodes induced by Josephson vortices collectively pinning is presented for well understanding the experimental observation of the reemergent superconductivity. This finding sheds light on an opportunity to search for the exotic FFLO state in the van der Waals heterostructures with strong interfacial spin-orbit coupling.

Interplay of the Spin Density Wave and a Possible Fulde-Ferrell-Larkin-Ovchinnikov State in CeCoIn_{5} in Rotating Magnetic Field

The d-wave superconductor CeCoIn_{5} has been proposed as a strong candidate for supporting the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state near the low-temperature boundary of its upper critical field. Neutron diffraction, however, finds spin-density-wave (SDW) order in this part of the phase diagram for field in the a-b plane, and evidence for the SDW disappears as the applied field is rotated toward the tetragonal c axis. It is important to understand the interplay between the SDW and a possible FFLO state in CeCoIn_{5}, as the mere existence of an SDW does not necessarily exclude an FFLO state. Here, based on a model constructed on the basis of available experiments, we show that an FFLO state competes with an SDW phase. The SDW state in CeCoIn_{5} is stabilized when the field is directed close to the a-b plane. When the field is rotated toward the c axis, the FFLO state emerges, and the SDW phase disappears. In the FFLO state, the nodal planes with extra quasiparticles (where the superconducting order parameter is zero) are perpendicular to the field, and in the SDW phase, the quasiparticle density of states is reduced. We test this model prediction by measuring heat transported by normal quasiparticles in the superconducting state. As a function of field, we observe a reduction of thermal conductivity for field close to the a-b plane and an enhancement of thermal conductivity when field is close to the c axis, consistent with theoretical expectations. Our modeling and experiments, therefore, indicate the existence of the FFLO state when field is parallel to the c axis.

Evidence for a Spatially Modulated Superfluid Phase of ^{3}He under Confinement

In superfluid ^{3}He-B confined in a slab geometry, domain walls between regions of different order parameter orientation are predicted to be energetically stable. Formation of the spatially modulated superfluid stripe phase has been proposed. We confined ^{3}He in a 1.1  μm high microfluidic cavity and cooled it into the B phase at low pressure, where the stripe phase is predicted. We measured the surface-induced order parameter distortion with NMR, sensitive to the formation of domains. The results rule out the stripe phase, but are consistent with 2D modulated superfluid order.

Temperature Controlled Fulde-Ferrell-Larkin-Ovchinnikov Instability in Superconductor-Ferromagnet Hybrids

We show that a wide class of layered superconductor-ferromagnet (S/F) hybrids demonstrates the emergence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase well below the superconducting transition temperature. By decreasing the temperature, one can switch the system from uniform to the FFLO state which is accompanied by the damping of the diamagnetic Meissner response down to zero and also by the sign change in the curvature of the current-velocity dependence. Our estimates show that an additional layer of the normal metal (N) covering the ferromagnet substantially softens the conditions required for the predicted FFLO instability, and for existing S/F/N systems, the temperature of the transition into the FFLO phase can reach several kelvins.

Inhomogeneous Superconductivity in Organic and Related Superconductors

Evidence of inhomogeneous superconductivity, in this case superconductivity with a spatially modulated superconducting order parameter, has now been found in many materials and by many measurement methods. Although the evidence is strong, it is circumstantial in the organic superconductors, scant in the pnictides, and complex in the heavy Fermions. However, it is clear some form of exotic superconductivity exists at high fields and low temperatures in many electronically anisotropic superconductors. The evidence is reviewed in this article, and examples of similar measurements are compared across different families of superconductors. An effort is made to find a consistent way to measure the superconducting energy gap across all materials, and use this value to predict the Clogston–Chandrasakhar paramagnetic limit Hp. Methods for predicting the existence of inhomogeneous superconductivity are shown to work for the organic superconductors, and then used to suggest new materials to study.

Thermodynamic Evidence for the Fulde-Ferrell-Larkin-Ovchinnikov State in the KFe_{2}As_{2} Superconductor

We investigate the magnetic phase diagram near the upper critical field of KFe_{2}As_{2} by magnetic torque and specific heat experiments using a high-resolution piezorotary positioner to precisely control the parallel alignment of the magnetic field with respect to the FeAs layers. We observe a clear double transition when the field is strictly aligned in the plane and a characteristic upturn of the upper critical field line, which goes far beyond the Pauli limit at 4.8 T. This provides firm evidence that a Fulde-Ferrell-Larkin-Ovchinnikov state exists in this iron-based KFe_{2}As_{2} superconductor.

Investigation of the superconducting gap structure in κ-(BEDT-TTF)2Cu(NCS)2 and κ-(BEDT-TTF)2Cu[N(CN)2]Br by means of thermal-conductivity measurements

We report temperature-dependent thermal-conductivity, κ, measurements on the layered quasi-two-dimensional organic superconductors κ-(BEDT-TTF)₂Cu(NCS)₂ and κ-(BEDT-TTF)₂Cu[N(CN)₂]Br down to 160 mK. The results for κ-(BEDT-TTF)₂Cu(NCS)₂ may be consistent with a nodal superconducting (SC) gap structure as indicated by a non-negligible remnant linear contribution when [Formula: see text] is extrapolated to [Formula: see text]. For κ-(BEDT-TTF)₂Cu[N(CN)₂]Br, contrary to expectations, higher κ values are observed in the superconducting regime as compared to the normal, high-field state evidencing a dominant phonon contribution to κ in the superconducting state. The strong increase of κ in the normal state below T _c for both samples indicates strong electron-phonon scattering. Our results highlight the need for thermal-conductivity measurements performed down to significantly lower temperatures to determine the symmetry of the SC gap.

Collective Modes of a Soliton Train in a Fermi Superfluid

We characterize the collective modes of a soliton train in a quasi-one-dimensional Fermi superfluid, using a mean-field formalism. In addition to the expected Goldstone and Higgs modes, we find novel long-lived gapped modes associated with oscillations of the soliton cores. The soliton train has an instability that depends strongly on the interaction strength and the spacing of solitons. It can be stabilized by filling each soliton with an unpaired fermion, thus forming a commensurate Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We find that such a state is always dynamically stable, which paves the way for realizing long-lived FFLO states in experiments via phase imprinting.

Frustrated magnets in high magnetic fields-selected examples

An indispensable parameter to study strongly correlated electron systems is the magnetic field. Application of high magnetic fields allows the investigation, modification and control of different states of matter. Specifically for magnetic materials experimental tools applied in such fields are essential for understanding their fundamental properties. Here, we focus on selected high-field studies of frustrated magnetic materials that have been shown to host a broad range of fascinating new and exotic phases. We will give brief insights into the influence of geometrical frustration on the critical behavior of triangular-lattice antiferromagnets, the accurate determination of exchange constants in the high-field saturated state by use of electron spin resonance measurements, and the coupling of magnetic degrees of freedom to the lattice evidenced by ultrasound experiments. The latter technique as well allowed new, partially metastable phases in strong magnetic fields to be revealed.