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.     

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 structure of the vortex lattice in anisotropic superconductors

The structure of the vortex lattice in anisotropic superconductors at an arbitrary temperature in magnetic fields close to critical was studied. Generally, a rhombohedral structure with a vertex angle depending on temperature, magnetic field, and material constants is formed. An important factor is the small (2%) difference of the free energies of the triangular and square lattices in the Ginzburg-Landau approximation. This factor also persists in anisotropic superconductors.     

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.     

Spatial line nodes and fractional vortex pairs in the Fulde-Ferrell-Larkin-Ovchinnikov vortex state of spin-singlet superconductors

A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a nontrivial solution for the FFLO vortex phase that exists near the upper critical field in which the wave function has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of nonparallel line nodes. We show that these solutions arise from the decay of conventional Abrikosov vortices into pairs of fractional vortices. We propose that neutron scattering studies can observe these fractional vortex pairs through the observation of a lattice of 1/2 flux quanta vortices. We also consider related phases in noncentrosymmetric superconductors.     

Local tunneling spectroscopy as a signature of the Fulde-Ferrell-Larkin-Ovchinnikov state in s- and d-wave superconductors

The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states for two-dimensional s- and d-wave superconductors (s- and d-SCs) are self-consistently studied under an in-plane magnetic field. While the stripe solution of the order parameter is found to have lower free energy in s-SCs, a square lattice solution appears to be energetically more favorable in the case of d-SCs. At certain symmetric sites, we find that the features in the local density of states (LDOS) can be ascribed to two types of bound states. We also show that the LDOS maps for d-SCs exhibit bias-energy-dependent checkerboard patterns. These characteristics can serve as signatures of the FFLO states.     

Competition between BCS and FFLO States in Magnetic Superconductors in a Cryptoferromagnetic Phase

The possibility of appearance of inhomogeneous superconducting Fulde—Ferrell—Larkin—Ovchinnikov (FFLO) states in magnetic superconductors in a cryptoferromagnetic phase with helical magnetic ordering has been analyzed. The dependence of the critical temperature on the angle between the wave vectors of the spatial modulation of the FFLO state and helical magnetic structure has been calculated within the proposed model. It has been shown that their mutually perpendicular orientation corresponds to the most energetically favorable state. The numerical calculations have also shown the existence of a tricritical point on a line separating the Bardeen—Cooper—Schrieffer and FFLO phases on the phase diagram of states. Furthermore, FFLO states can appear in a magnetic superconductor even at fairly strong exchange fields because of the difference between the effective masses of conduction electrons in different spin subbands and the anisotropy of the Fermi surface.

     

Symmetry of the superconducting order parameter in frustrated systems determined by the spatial anisotropy of spin correlations

We study the resonating valence bond theory of the Hubbard-Heisenberg model on the half-filled anisotropic triangular lattice. Varying the frustration changes the wave vector of maximum spin correlation in the Mott insulating phase. This, in turn, changes the symmetry of the superconducting state that occurs at the boundary of the Mott insulating phase. We propose that this physics is realized in several families of quasi-two-dimensional organic superconductors.     

Vortex liquid crystals in anisotropic type II superconductors

In an isotropic type II superconductor in a moderate magnetic field, the transition to the normal state occurs by vortex lattice melting. In certain anisotropic cases, the vortices acquire elongated cross sections and interactions. Systems of anisotropic, interacting constituents generally exhibit liquid crystalline phases. We examine the possibility of a two step melting in homogeneous type II superconductors with anisotropic superfluid stiffness from a vortex lattice into first a vortex smectic and then a vortex nematic at high temperature and magnetic field. We find that fluctuations of the ordered phase favor an instability to an intermediate smectic-A in the absence of intrinsic pinning.     

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.     

Effects of edge boundaries on Josephson vortices in finite-size layered high-Tc superconductors

In order to systematically explain the in-plane size effects for the periodical dependence of the Josephson-vortex-flow resistance on the magnetic field, we numerically explore static lattice structures of Josephson vortices in layered high-Tc superconductors with finite in-plane sizes from sub-microm to more than 10 microm by simulating slow quenching processes from high temperature under the magnetic field. The numerical results reveal that in sub-microm size the rectangular lattice is a widely spread major structure in H-T diagram and the triangular lattice is a minor one which emerges only around the specific magnetic field supplying n(phi)0 per one junction area. These results suggest that sub-microm size layered high-Tc superconductors are promising for future device applications.     

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.     

Van der Waals interaction between flux lines in high- superconductors: A variational approach

In pure anisotropic or layered superconductors thermal fluctuations induce a van der Waals attraction between flux lines. This attraction together with the entropic repulsion has interesting consequences for the low field phase diagram; in particular, a first order transition from the Meissner phase to the mixed state is induced. We introduce a new variational approach that allows for the calculation of the effective free energy of the flux line lattice on the scale of the mean flux line distance a, which is based on an expansion of the free energy around the regular triangular Abrikosov lattice. Using this technique, the low field phase diagram of these materials may be explored. The results of this technique are compared with a recent functional RG treatment of the same system. Received: 25 June 1996 / Revised: 18 August 1998 / Accepted: 21 August 1998     

Test for pairing symmetry based on spin fluctuations in the organic superconductor kappa-(BEDT-TTF)2X

We propose that the superconducting pairing symmetry of organic superconductors kappa-(BEDT-TTF)2X can be determined by measuring the position in momentum space of the incommensurate peaks of the spin susceptibility. Using the weak coupling BCS theory and including the many-body effects via the random-phase approximation for the Hubbard model on an anisotropic triangular lattice, we show that the position of these peaks is uniquely determined by the pairing symmetry of the superconducting state and the geometry of the Fermi surface. We demonstrate the different incommensurate patterns of spin responses for d(x(2)-y(2-)) and d(xy)-like pairing states. In addition, we find that there is no spin resonance mode in the reasonable range of parameters discussed.     

Variational Monte Carlo study of the nematic state in iron-pnictide superconductors with a five-orbital model

We perform a variational Monte Carlo study of the nematic state in iron-pnictide superconductors within a realistic five-orbital model.Our numerical results show that the nematic state,formed by introducing an anisotropic hopping order into the projected wave function,is not stable unless the off-site Coulomb interaction V exceeds a critical value.This demonstrates that V plays a key role in forming the nematic state in iron-pnictide superconductors.In the nematic state,the orbital order and the anisotropic spin correlations are consistent with the experimental observations.We argue that the experimentally observed anisotropic magnetic couplings and structural transition are associated with the nematic state and can be understood in a unified framework.     

High-pressure effect on the crystal and magnetic structure of LuMnO3: Correlation between a distortion of the triangular lattice and the symmetry of the magnetic state in hexagonal frustrated manganites

The effect of a high pressure (up to 6 GPa) on the crystal and magnetic structure of the hexagonal manganite LuMnO₃ is studied by neutron diffraction in the temperature range 10–295 K. It is found that, as the pressure increases, the ordered magnetic moment of Mn ions at T = 10 K decreases noticeably from 2.48 (0 GPa) to 1.98 μ_B (6 GPa). This decrease is due to an enhancement of the geometrical frustration effects on the triangular lattice. At the same time, the symmetry of the triangular antiferromagnetic state (the irreducible representation Γ₂) remains unchanged. A correlation is revealed between the distortion parameter of the triangular lattice formed by Mn ions and the symmetry of the antiferromagnetic state of hexagonal manganites RMnO₃. Based on this correlation, a generalized magnetic phase diagram of these compounds is constructed. The obtained phase diagram provides an explanation for the changes observed in the magnetic state of hexagonal manganites caused by high pressure and chemical substitution.     

Structure of Flux Line Lattices in Tilt Magnetic Fields of Anisotropic Superconductos

We study here, by the minimization of the total energy of flux line systems, the zero temperature structure of flux lines of uniaxial anisotropic superconductors in a tilt magnetic field. The anisotropic London model is used and an efficient method is developed to make the total energy calculation manageable. Two degenerate structures are found, one is a deformed triangular structure and the other is a superlattice with three lines per unit cell.     

Ordering in spatially anisotropic triangular antiferromagnets

We investigate the phase diagram of the anisotropic spin-1/2 triangular lattice antiferromagnet, with interchain diagonal exchange J' much weaker than the intrachain exchange J. We find that fluctuations lead to a competition between (commensurate) collinear antiferromagnetic and (zigzag) dimer orders. Both states differ in symmetry from the spiral order known to occur for larger J', and are therefore separated by quantum phase transitions from it. The zero-field collinear antiferromagnet is succeeded in a magnetic field by magnetically ordered spin-density-wave and cone phases, before reaching the fully polarized state. Implications for the anisotropic triangular magnet Cs2CuCl4 are discussed.     

Magnetoelastic coupling and symmetry breaking in the frustrated antiferromagnet alpha-NaMnO2

The magnetic and crystal structures of the alpha-NaMnO2 have been determined by high-resolution neutron powder diffraction. The system maps out a frustrated triangular spin lattice with anisotropic interactions that displays two-dimensional spin correlations below 200 K. Magnetic frustration is lifted through magneto-elastic coupling, evidenced by strong anisotropic broadening of the diffraction profiles at high temperature and ultimately by a structural phase transition at 45 K. In this low-temperature regime a three-dimensional antiferromagnetic state is observed with a propagation vector k=(1/2,1/2,0).     

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.