Electron-hole pairing with nonzero momentum in a graphene bilayer

Electron-hole pairing due to the Coulomb interaction in the system of two graphene sheets has been considered. The critical transition temperature has been determined as a function of both the distance between the electron and hole Fermi lines and the triangular distortion of their spectrum. It has been shown that when the distance between Fermi lines is longer than a critical value, the temperature of the transition to a state with nonzero momentum of Cooper pairs (Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state) is higher than the temperature of the transition to the Bardeen-Cooper-Schrieffer state. The Josephson effect for the FFLO state has been analyzed, which is due to the tunneling of charge carriers between the graphene sheets. It has been shown that the spatial structure of the order parameter of the system in this state can be reconstructed, i.e., the FFLO state can be identified from the dependence of the tunneling current on the magnetic field parallel to the graphene sheets. Other experimental methods for studying the phase diagram of the system have been discussed.     

FFLO States in Layered Organic Superconductors

In this short review, the recently found experimental evidence that Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states are realized in quasi‐two‐dimensional (2D) organic superconductors is reported. At low temperatures and when a high magnetic field is aligned parallel to the conducting organic layers, an upturn of the upper critical field much beyond the Pauli limit is observed, as proven by thermodynamic measurements. Under certain conditions, a second thermodynamic transition emerges inside the FFLO state. Nuclear magnetic resonance (NMR) work has added strong microscopic support for the realization of the FFLO state. The NMR spectra in the FFLO phase can very well be explained by a nonuniform one‐dimensionally modulated superconducting order parameter. All these features, appearing only in a very narrow angular region close to parallel‐field orientation, give robust evidence for the realization of the FFLO state in organic superconductors.     

The Gor'kov and Melik-Barkhudarov Correction to the Mean-Field Critical Field Transition to Fulde–Ferrell–Larkin–Ovchinnikov States

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states, characterized by Cooper pairs condensed at finite-momentum are, at the same time, exotic and elusive. It is partially due to the fact that the FFLO states allow superconductivity to survive even in strong magnetic fields at the mean-field level. The effects of induced interactions at zero temperature are calculated in both clean and dirty cases, and it is found that the critical field at which the quantum phase transition to an FFLO state occurs at the mean-field level is strongly suppressed in imbalanced Fermi gases. This strongly shrinks the phase space region where the FFLO state is unstable and more exotic ground state is to be found. In the presence of high level impurities, this shrinkage may destroy the FFLO state completely.     

Quantum phase transition of the Fulde–Ferrell–Larkin–Ovchinnikov states in two-dimensional anisotropic triangular system

Based on the Bogoliubov de Gennes (BdG) equations, we study the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) states for d-wave superconductor in anisotropic triangular system self-consistently with a strong magnetic field applied parallel to its conducting planes. We find that the two-dimensional FFLO state transforms to one-dimensional FFLO state as the system frustrated. The calculated local density of states are suggested to distinguish these states.     

Reentrant phases in compensated ferrocholesterics

Influence of magnetic field on orientation and magnetic properties of a compensated ferrocholesteric, a suspension of needle-like ferromagnetic particles in a cholesteric liquid crystal, was studied theoretically. A phase transition from a ferrocholesteric to a ferronematic state in a magnetic field oriented normally to the axis of the helical structure was considered. The dependences of the transition field to the ferronematic phase on the material parameters of the suspension and of the helical structure pitch and magnetization on the field strength were investigated. A possibility of existence of a reentrant ferrocholesteric phase was shown.

     

Fulde-Ferrell-Larkin-Ovchinnikov state in a perpendicular field of quasi-two-dimensional CeCoIn5

A Fulde-Ferrell-Larkin-Ovchinnkov (FFLO) state was previously reported in the quasi-2D heavy fermion CeCoIn5 when a magnetic field was applied parallel to the ab plane. Here, we conduct 115In NMR studies of this material in a perpendicular field, and provide strong evidence for FFLO in this case as well. Although the topology of the phase transition lines in the H-T phase diagram is identical for both configurations, there are several remarkable differences between them. Compared to H parallelab, the FFLO phase for H perpendicularab is confined in a much narrower region at the low-T-high-H corner in the H-T plane, and the critical field separating the FFLO and non-FFLO superconducting states almost ceases to have a temperature dependence. Moreover, directing H perpendicularab results in a notable change in the quasiparticle excitation spectrum within the planar node associated with the FFLO transition.     

Magnetic field effect on the pairing state competition in quasi-one-dimensional organic superconductors (TMTSF)2X

We study the effect of the magnetic field on the pairing state competition in organic conductors (TMTSF)₂X by applying random phase approximation to a quasi-one-dimensional extended Hubbard model. We show that the singlet pairing, triplet pairing and the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) superconducting states may compete when charge fluctuations coexist with spin fluctuations. This rises a possibility of a consecutive transition from singlet pairing to FFLO state and further to S_z = 1 triplet pairing upon increasing the magnetic field. We also show that the singlet and S_z = 0 triplet components of the gap function in the FFLO state have “d-wave” and “f-wave” forms, respectively, which are strongly mixed.     

Possible Fulde-Ferrell-Larkin-Ovchinnikov inhomogeneous superconducting state in CeCoIn5

We present specific heat and thermal conductivity of the heavy fermion superconductor CeCoIn5 in the vicinity of the superconducting critical fieldH _c2, measured with magnetic field in the plane of this quasi-2D compound and at temperatures down to 50 mK. The superconducting phase diagram and the first order nature of the superconducting phase transition at high fields close to a critical fieldH _c2 indicate the importance of the Pauli limiting effect in CeCoIn₅. In the same range of magnetic field we observe a second specific heat anomaly within the superconducting state, and interpret it as a signature of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) inhomogeneous superconducting state. In addition, the thermal conductivity data as a function of field display a kink at a fieldH _k below the superconducting critical field, which closely coincides with the low temperature anomaly in specific heat tentatively identified with the appearance of the FFLO superconducting state. The enhancement of thermal conductivity within the FFLO state calls for further theoretical investigations of the real space structure of the order parameter (and in particular, the structure of vortices) and of the thermal transport within the inhomogeneous FFLO state.     

Evolution of paramagnetic quasiparticle excitations emerged in the high-field superconducting phase of CeCoIn5

We present (115)In NMR measurements in a novel thermodynamic phase of CeCoIn(5) in a high magnetic field, where exotic superconductivity exists with the incommensurate spin-density wave order. We show that the NMR spectra in this phase provide direct evidence for the emergence of the spatially distributed normal quasiparticle regions. The quantitative analysis for the field evolution of the paramagnetic magnetization and newly emerged low-energy quasiparticle density of states is consistent with the nodal plane formation, which is characterized by an order parameter in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The NMR spectra also suggest that the spatially uniform spin-density wave is induced in the FFLO phase.     

Observation of spin susceptibility enhancement in the possible Fulde-Ferrell-Larkin-Ovchinnikov state of CeCoIn(5)

We report (115)In nuclear magnetic resonance measurements of the heavy-fermion superconductor CeCoIn(5) in the vicinity of the superconducting critical field H(c2) for a magnetic field applied perpendicular to the ? axis. A possible inhomogeneous superconducting state, the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, is stabilized in this part of the phase diagram. In an 11 T applied magnetic field, we observe clear signatures of the two phase transitions: the higher temperature one to the homogeneous superconducting state and the lower temperature phase transition to a FFLO state. We find that the spin susceptibility in the putative FFLO state is significantly enhanced as compared to the value in a homogeneous superconducting state. The implications of this finding for the nature of the low temperature phase are discussed.     

Phase diagram of a surface superconductor in parallel magnetic field

The universal phase diagram of a 2D surface superconductor with generic Rashba interaction in a parallel magnetic field is found. In addition to the uniform BCS state, we find two inhomogeneous superconductive states, the stripe phase with Δ (r) ∝ cos(Qr) at high magnetic fields, and a new “helical” phase with Δ(r) ∝ exp(iQr) which intervenes between the BCS state and stripe phase at an intermediate magnetic field and temperature. We prove that the ground state for helical phase carries no current.     

Phase transition in antiferromagnets with anisotropic exchange interactions and uniaxial anisotropy

Abstract

Following the Bogoliubov variational principle, the equilibrium and stability equations of the free energy for the two sublattice antiferromagnetic system with inter- and intrasublattice exchange interactions and with an external magnetic field are investigated. For the Ising spin system with uniaxial anisotropy, the phase diagrams have been calculated for various values of anisotropy constant d and the ratio of intra- to intersublattice interaction constants γ. It is shown that first-order, as well as second-order transitions, occur for γ > 0, whereas only a second-order transition occurs for γ ≦ 0, irrespective of the sign of d. Furthermore, similar calculations are extended for the anisotropic Heisenberg spin system and quite interesting phase diagrams have been obtained. Next, the effects of the anisotropic exchange interactions on the magnetic ordered states and the magnetizations of the singlet ground state system of spin one and with a uniaxial anisotropy term are investigated in the vicinity of the level crossing field H ? D/gμ _B . A field-induced ordered state without the transverse component of magnetization is shown to appear in a certain range of magnetic field as the spin dimensionality decreases. It has also turned out that the phase transition between this ordered state and the canted antiferromagnetic state ordinarily found for the isotropic singlet ground state system is of first order. Lastly, the stable spin configurations at a temperature of absolute zero for a two-sublattice uniaxial antiferromagnet under an external magnetic field of arbitrary direction are studied. In particular, the effects of a single ionic anisotropy D-term and anisotropy in the exchange interactions on the magnetic phases are investigated. The antiferromagnetic state has turned out to appear only for the external magnetic field along the easy axis of sublattice magnetization, and makes a first-order phase transition to the canted-spin state or the ferromagnetic state. For other field directions, no antiferromagnetic state appears and only a second-order phase transition between the canted-spin and the ferromagnetic states occurs. The critical field as a function of external field direction has been calculated for several D-values.     

A possibility of a new type of the Fulde-Ferrell-Larkin-Ovchinnikov state

We propose a new type of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state with a cylindrical symmetric order-parameter. We study the Ginzburg-Landau (GL) theory of the strongly Pauli limited type II superconductor with a spherical symmetric fermi surface, near the critical magnetic field of the FFLO state in the ground state. We find that the cylindrical state has a lower energy than the stripe state, which has the lowest energy in the states examined so far.     

Pressure dependence of the Fulde-Ferrell-Larkin-Ovchinnikov state in CeCoIn5

Pressure studies of the thermodynamics of CeCoIn5 under magnetic fields H parallel to c and H parallel to ab have been made up to P = 1.34 GPa. We recorded the signature of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state for all pressures when H parallel to ab. Also remarkably, the FFLO regime suddenly expands for P = 1.34 GPa. With the help of a microscopic theory for d-wave superconductivity, we have extracted the gyromagnetic ratio g and the Fermi velocities nu(a) and nu(c). Our study is the first evidence for the existence of the FFLO state away from the influence of the antiferromagnetic fluctuations. We find a close parallel between the T-P phase diagram of CeCoIn5 and the T-x phase diagram of the high-Tc cuprates, where x is the hole concentration.     

The Fulde-Ferrell-Larkin-Ovchinnikov states in s and d-wave superconductor with spin-dependent bandwidth imbalance on square lattice

We study numerically the phase diagram for s and d-wave fermionic superfluidity/superconductivity with spin-dependent bandwidth imbalance on a two-dimensional square-lattice. We also investigate the spontaneous space symmetry breaking states at low temperatures by solving the Bogoliubov-de Gennes equations. It is found that, the spatial configuration of the order parameter,both the uni-directional Fulde-Ferrell-Larkin-Ovchinnikov(FFLO) states and the two-dimensional FFLO state may show up in the presence of finite spin-dependent bandwidth imbalance. Moreover, we calculate the spectra of local density of states, and the experimental proposals of observing such FFLO states are therefore suggested.     

Novel route to a finite center-of-mass momentum pairing state for superconductors: A current-driven Fulde-Ferrell-Larkin-Ovchinnikov state

The previously studied Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is stabilized by a magnetic field via the Zeeman coupling in spin-singlet superconductors. Here we suggest a novel route to achieve nonzero center-of-mass momentum pairing states in superconductors with Fermi surface nesting. We investigate two-dimensional superconductors under a uniform external current, proportional to a finite pair momentum of q(e). We find that an FFLO state with a spontaneous pair momentum of q(s) is stabilized above a certain critical current that depends on the direction of the external current. A finite q(s) arises in order to make the total pair-momentum of q(t)(=q(s) + q(e)) perpendicular to the nesting vector, which is independent of spin states of Cooper pairs. We also discuss experimental signatures of the FFLO state.     

Exploring the relationship between the magnetic frustration and the emergence of FFLO state on a triangular lattice

The Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) unconventional superconductors attract renewed interest in recent years. However, an unambiguous experimental demonstration of the FFLO state is hindered by the stringent requirements for its realization. In this paper, we explore the relationship between the magnetic frustration and the emergence of the FFLO state on an anisotropic triangular lattice, based on the self-consistent calculation of the Bogoliubov-de Gennes equations. We find that the required lower critical magnetic field to enter the FFLO state decreases with the increase of both the anisotropic ratio and the on-site Coulomb repulsive interaction. This demonstrates that it is easier to enter the FFLO state on the structurally frustrated triangular lattice in comparison with the square lattice, and suggests that the layered organic superconductors with a triangular lattice may be good candidates for exploring the FFLO state.     

Antivortices due to competing orbital and paramagnetic pair-breaking effects

Thermodynamically stable vortex—antivortex structures in a quasi-twodimensional superconductor in a tilted magnetic field are predicted. For this geometry, both orbital and spin pair-breaking effects exist, with their relative strength depending on the tilt angle θ. The spectrum of possible states contains the ordinary vortex state (for large θ) and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state (for θ = 0) as limits. The quasi-classical equations are solved nearH _c2 for arbitrary θ and it is shown that stable states with co-existing vortices and antivortices exist in a small interval close to θ= 0. The results are compared with recent predictions of antivortices in mesoscopic samples.     

Large triplet pairing mixing in the FFLO state of spin fluctuation mediated superconductivity in Q1D systems

We study the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO) state of spin fluctuation mediated superconductivity and focus on the effect of coexisting charge fluctuations. We find that (i) consecutive transitions from singlet pairing to FFLO and further to S_z=1 triplet pairing can generally take place upon increasing the magnetic field when strong charge fluctuations coexist with spin fluctuations and (ii) the enhancement of the charge fluctuations lead to a significant increase of the parity mixing in the FFLO state, where the triplet/singlet component ratio in the gap function can be close to unity. We propose that such consecutive pairing state transition and strong parity mixing in the FFLO state may take place in a quasi-one-dimensional organic superconductor (TMTSF)₂X.     

Enhancing of the critical temperature of an in-plane FFLO state in heterostructures by the orbital effect of the magnetic field

It is well-known that the orbital effect of the magnetic field suppresses superconducting T _c . We show that for a system, which is in the Larkin-Ovchinnikov-Fulde-Ferrell (FFLO) state at zero external magnetic field, the orbital effect of an applied magnetic field can lead to the enhancement of the critical temperature higher than T _c at zero field. We concentrate on two systems, where the in-plane FFLO state was predicted recently. These are equilibrium S/F bilayers and S/N bilayers under nonequilibrium quasiparticle distribution. However, it is suggested that such an effect can take place for any plane superconducting system, which is in the in-plane FFLO state (or is close enough to it) at zero applied field.