We study the phase diagram of a superconducting ring threaded by an Aharonov-Bohm flux and an in-plane magnetic Zeeman field. The simultaneous presence of both the external flux and the in-plane magnetic field leads to the competition between the Fulde-Ferrell (FF) phase and the Larkin-Ovchinnikov (LO) phase. Using the Bogoliubov-de Gennes equation, we investigate the spacial profile of the order parameter. Both the FF phase and the LO phase are found to exist stably in this system. The phase boundary is determined by comparing the free energy. The distortion of the phase diagrams due to the mesoscopic effect is also studied.
Fe-based superconductors (FeSC) exhibit all the properties of systems that allow the formation of a superconducting phase with oscillating order parameter, called the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase. By the analysis of the Cooper pair susceptibility in two-band FeSC, such systems are shown to support the existence of a FFLO phase, regardless of the exhibited order parameter symmetry. We also show the state with nonzero Cooper pair momentum, in superconducting FeSC with $\sim \cos(k_{x}) \cdot \cos (k_{y})$ symmetry, to be the ground state of the system in a certain parameter r…
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…
Incommensurate antiferromangetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor is investigated on the basis of the Ginzburg-Landau theory. We formulate the two component Ginzburg-Landau model to discuss two degenerate incommensurate AFM states in the tetragonal crystal structure. Owing to the broken translation symmetry in the FFLO state, a multiple phase diagram of single-q phase and double-q phase is obtained under the magnetic field along [100] or [010] direction. Magnetic properties in each phase are investigated and compared with the neutron scattering and NMR …
We report upper critical field measurements in the metal-free-all-organic superconductor $β''$-(ET)$_{2}$SF$_{5}$CH$_{2}$CF$_{2}$SO$_{3}$ obtained from measuring the in-plane penetration depth using the tunnel diode oscillator technique. For magnetic field applied parallel to the conducting planes the low temperature upper critical fields are found to exceed the Pauli limiting field calculated by using a semi-empirical method. Furthermore, we found a signature that could be the phase transition between the superconducting vortex state and the Fulde-Ferrell-Larkin-Ovchinnikov state in the form …
The antiferromagnetic Fulde-Ferrell-Larkin-Ovchinnikov (AFM-FFLO) state of coexisting d-wave FFLO superconductivity and incommensurate AFM order is studied on the basis of Bogoliubov-de Gennes (BdG) equations. We show that the incommensurate AFM order is stabilized in the FFLO state by the appearance of the Andreev bound state localized around the zeros of the FFLO order parameter. The AFM-FFLO state is further enhanced by the induced π-triplet superconductivity (pair density wave). The AFM order occurs in the FFLO state even when it is neither stable in the normal state nor in the BCS state. …
The antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state is analyzed on the basis of a Ginzburg-Landau theory. To examine the possible AFM-FFLO state in CeCoIn_5, we focus on the incommensurate AFM order characterized by the wave vector Q = Q_{0} \pm q_inc with Q_0 =(π,π,π) and q_inc \parallel [110] or [1-10] in the tetragonal crystal structure. We formulate the two component Ginzburg-Landau theory and investigate the two degenerate incommensurate AFM order. We show that the pinning of AFM moment due to the FFLO nodal planes leads to multiple phase…
We demonstrate that the vortex state in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase may be very different depending on the field orientation relative to the crystalline axes. We calculate numerically the upper critical field near the tricritical point taking into account the modulation of the order parameter along the magnetic field as well as the higher Landau levels. For s-wave superconductors with the anisotropy described by an elliptical Fermi surface we propose a general scheme of the analysis of the angular dependence of upper critical field at all temperatures on the basis of the …
The exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states have been actively searched for experimentally since the mean-field based FFLO theories were put forward half a century ago. Here we investigate the stability of FFLO states against unavoidable pairing fluctuations, and conclude that FFLO superfluids cannot exist due to their intrinsic instability in three and two dimensions. This explains their absence in experimental observations in both condensed matter systems and the most recent, more promising ultracold atomic Fermi gases with a population imbalance.
We consider the density response of a spin-imbalanced ultracold Fermi gas in an optical lattice in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We calculate the collective mode spectrum of the system in the generalised random phase approximation and find that though the collective modes are damped even at zero tempererature, the damping is weak enough to have well-defined collective modes. We calculate the speed of sound in the gas and show that it is anisotropic due to the anisotropy of the FFLO pairing, which implies an experimental signature for the FFLO state.
The recent experimental support for the presence of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the CeCoIn5 directed the attention towards the mechanisms responsible for this type of superconductivity. We investigate the FFLO state in a model where on--site/inter--site pairing coexists with repulsive pair hopping interaction. The latter interaction is interesting in that it leads to pairing with nonzero momentum of the Cooper pairs even in the absence of the external magnetic field (the so-called eta-pairing). It turns out that depending on the strength of the pair hopping interaction…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, characterized by Cooper pairs condensed at finite momentum, has been a long-sought state that remains unresolved in many classes of fermionic systems, including superconductors and ultracold atoms. A fascinating aspect of the FFLO state is the emergence of periodic nodal planes in real space, but its observation is still lacking. Here we investigate the superconducting order parameter at high magnetic fields $H$ applied perpendicular to the $ab$ plane in a high-purity single crystal of FeSe. The heat capacity and magnetic torque provide thermo…
The properties of incommensurate antiferromagnetic (AFM) order in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is studied by solving the Bogoliubov-de-Gennes (BdG) equations. The relationship between the electronic structure and the magnetic structure is clarified. We find that the magnetic structure in the AFM-FFLO state includes three cases. (I) In the strongly localized case, the AFM staggered moment is confined into the FFLO nodal planes where the superconducting order parameter vanishes. (II) In the weakly localized case, the AFM staggered moment appears in the whole spatial region, …
In nonuniform Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) superconductors, both the gauge symmetry and the continuous translational symmetry of the normal state are spontaneously broken. This leads to additional bosonic excitations, or Goldstone modes, corresponding to the deformations of the order parameter amplitude modulation in real space. We derive general expressions for the energy of the phase and elastic Goldstone modes. As an example, the superfluid density and the elastic modulus of a one-dimensional LOFF superconductor are calculated at low temperatures.
We study superconducting properties of population-imbalanced ultracold Fermi mixtures in the honeycomb lattice that can be effectively described by the spin-imbalanced attractive Hubbard model in the presence of a Zeeman magnetic field. We use the mean-field theory approach to obtain ground state phase diagrams including some unconventional superconducting phases such as the Fulde--Ferrell--Larkin--Ovchinnikov (FFLO) phase. We show that this phase is characterized by atypical behaviour of the Cooper pairs total momentum in the external magnetic field. We show that the momentum changes its valu…
We study the interplay between the Zeeman field and spin-orbit coupling (SOC) in harmonically trapped Fermi gases loaded into a two-dimensional single-band tight-binding optical lattice. Using the Bogoliubov-de Gennes theory, we find that the Zeeman field combined with a Rashba SOC gives rise to $(i)$ Fulde-Ferrell-like superfluidity and $(ii)$ skyrmion-like polarization textures near the edges of the system. We also discussed the effects of interaction, temperature, SOC anisotropy and Zeeman field anisotropy on the superfluid ground state and polarization textures.
Bosonization and density-matrix renormalization group studies of Fulde-Ferrell-Larkin-Ovchinnikov phase and irrational magnetization plateaus in coupled chains
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase is an unconventional superconducting state found under the influence of strong Zeeman field. This phase is identified by finite center-of-mass momenta in the Cooper pairs, causing the pairing amplitude to oscillate in real space. Repulsive correlations, on the other hand, smear out spatial inhomogeneities in d-wave superconductors. We investigate the FFLO state in a strongly correlated d-wave superconductor within a consolidated framework of Hartree-Fock-Bogoliubov theory and Gutzwiller approximation. We find that the profound effects of strong…
In this work, the thermodynamic properties of the organic superconductor $λ$-(BETS)$_2$GaCl$_4$ are investigated to study a high-field superconducting state known as the putative Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We observed a small thermodynamic anomaly in the field $H_{\rm FFLO}$ $\sim$ 10~T, which corresponds to the Pauli limiting field $H_{\rm P}$. This anomaly probably originates from a transition from a uniform superconducting state to the FFLO state. $H_{\rm FFLO}$ does not show a strong field-angular dependence due to a quasi-isotropic paramagnetic effect in $λ$-(BETS)$_2$…
We show that the behaviour of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors near a surface is considerably different from the usual case. The order parameter of the FF state is strongly deformed near the surface, which leads to a number of unusual features in the linear magnetic response, such as "anti-screening" or "over-screening" of the applied field. In a fully isotropic FF case, the Meissner effect is still present, despite the vanishing of the transverse superfluid density in the bulk. We also calculate the surface critical field Hc3, which exhibits a peculiar temperature d…
We studied the phase diagram for a two-dimensional d-wave superconducting system under an in-plane magnetic field or an exchange field. According to the spatial configuration of the order parameter, we show that there exists quantum phase transitions in which the uniform phase transforms to the one-dimensional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, and then to two-dimensional FFLO state upon increasing the exchange field. The local density of states are calculated and suggested to be signatures to distinguish these phases.
We study attractively interacting spin-1/2 fermions on the square lattice subject to a spin population imbalance. Using unbiased diagrammatic Monte Carlo simulations we find an extended region in the parameter space where the Fermi liquid is unstable towards formation of Cooper pairs with non-zero center-of-mass momentum, known as the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In contrast to earlier mean-field and quasi-classical studies we provide quantitative and well-controlled predictions on the existence and location of the relevant Fermi-liquid instabilities. The highest temperature …
We present a full phase diagram for the one-dimensional (1D) to three-dimensional (3D) crossover of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in an attractive Hubbard model of 3D-coupled chains in a har- monic trap. We employ real-space dynamical mean-field theory which describes full local quantum fluctuations beyond the usual mean-field and local density approximation. We find strong dimensionality effects on the shell structure undergoing a crossover between distinctive quasi-1D and quasi-3D regimes. We predict an optimal regime for the FFLO state that is considerably extended to in…
We derive the fluctuational magnetization and the paraconductivity of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductors in their normal state. The FFLO superconducting fluctuations induce oscillations of the magnetization between diamagnetism and unusual paramagnetism which originates from the competition between paramagnetic and orbital effects. We also predict a strong anisotropy of the paraconductivity when the FFLO transition is approached in contrast with the case of a uniform BCS state. Finally building a Ginzburg-Levanyuk argument, we demonstrate that these fluctuation effects can…
We study the phase diagram in a two-dimensional Fermi gas with the synthetic spin-orbit coupling that has recently been realized experimentally. In particular, we characterize in detail the properties and the stability region of the unconventional Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in such a system, which are induced by spin-orbit coupling and Fermi surface asymmetry. We identify several distinct nodal FFLO states by studying the topology of their respective gapless contours in momentum space. We then examine the phase structure and the number density distributions in a typical har…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of a two-dimensional (2D) orthorhombic lattice superconductor is studied based on the Bogoliubov-de-Gennes equations. It is illustrated that the 2D FFLO state is suppressed and only one-dimensional (1D) stripe state is stable. The stripe changes its orientation with the increasing Zeeman field. There exists a crossover region where the gap structure has some local 2D features. These results are significantly different from those of the tetragonal lattice system. The local density of states is also studied which can be checked and compared with …
Recent study on doping effects in the heavy fermion superconductor CeCoIn$_5$ has shown that a small amount of doping induces unexpectedly large broadening of the second order transition into the high field and low temperature (HFLT) phase of this material. Motivated by this observation, effects of quenched disorder on the second order transition into a longitudinal Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state are examined. The observed large broadening of the transition is naturally explained as a consequence of softness of each FFLO nodal plane. The present results strongly support the scen…
We explore superconducting instability for a clean two-band layered superconductor with deep and shallow bands in the magnetic field applied perpendicular to the layers. In the shallow band, the quasiclassical approximation is not applicable, and Landau quantization has to be accounted for exactly. The electronic spectrum of this band in the magnetic field is composed of the one-dimensional Landau-level minibands. With increasing magnetic field the system experiences series of Lifshitz transitions when the chemical potential enters and exits the minibands. These transitions profoundly influenc…
We consider a two-component Fermi gas in the presence of spin imbalance, modeling the system in terms of a one-dimensional attractive Hubbard Hamiltonian initially in the presence of a confining trap potential. With the aid of the time-evolving block decimation method, we investigate the dynamics of the initial state when the trap is switched off. We show that the dynamics of a gas initially in the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) state is decomposed into the independent expansion of two fluids, namely the paired and the unpaired particles. In particular, the expansion velocity of the un…
We study the angular Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, in which the rotation symmetry is spontaneously broken, in population imbalanced fermion gases. The superfluid gases at near T=0 are investigated on the basis of the Bogoliubov-de Gennes (BdG) equation. We find that the angular FFLO state is stabilized in the gases confined in the toroidal trap, but not in the harmonic trap. We discuss the mechanism of the angular FFLO state based on the self-one-dimensionalization of the superfluid gas.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the vortex lattice state is quantitatively studied using the selfconsistent Eilenberger theory in three-dimensional (3D) space. We estimate free energy to determine the FFLO phase diagram in the H-T plane and stable FFLO wave number in the isotropic system with the 3D Fermi sphere and s-wave pairing. To facilitate the experimental identification of the FFLO state, we investigate the field evolution of NMR spectra and flux line lattice form factors obtained in neutron scattering in the FFLO vortex states. Possible applications of our results …
Ultracold two-component Fermi gases with a tunable population imbalance have provided an excellent opportunity for studying the exotic Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states, which have been of great interest in condensed matter physics. However, the FFLO states have not been observed experimentally in Fermi gases in three dimensions (3D), possibly due to their small phase space volume and extremely low temperature required for an equal-mass Fermi gas. Here we explore possible effects of mass imbalance, mainly in a $^6$Li--$^{40}$K mixture, on the one-plane-wave FFLO phases for a 3D ho…
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…
