We study the Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) superconducting state in the disordered systems. We analyze the microscopic model, in which the d-wave superconductivity is stabilized near the antiferromagnetic quantum critical point, and investigate two kinds of disorder, namely, box disorder and point disorder, on the basis of the Bogoliubov-deGennes (BdG) equation. The spatial structure of modulated superconducting order parameter and the magnetic properties in the disordered FFLO state are investigated. We point out the possibility of "FFLO glass" state in the presence of strong point disorders, which arises from the configurational degree of freedom of FFLO nodal plane. The distribution function of local spin susceptibility is calculated and its relation to the FFLO nodal plane is clarified. We discuss the NMR measurements for CeCoIn_5.
We derive the Ginzburg-Landau theory of unconventional singlet superconductors in the presence of a Zeeman field and impurities, in order to examine the resulting Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phases. We show that the behavior of the FFLO phases in unconventional superconductors in the presence of impurities is qualitatively different from that found for s-wave superconductors.
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 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 m…
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…
The first observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconducting state and a subsequent detection of the spin-dependent effective masses of quasiparticles in the CeCoIn_5 heavy fermion system are combined into a single theoretical framework. The appearance of the spin-split masses extends essentially the regime of temperatures and applied magnetic fields, in which FFLO is observable and thus is claimed to be very important for the FFLO detectability. We also stress that the quasiparticles composing Cooper pair become distinguishable in the nonzero field. The analysis is per…
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 …
A Zeeman magnetic field can induce a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in spin-singlet superconductors. Here we argue that there is a non-trivial solution for the FFLO vortex phase that exists near the upper critical field in which the wavefunction has only spatial line nodes that form intricate and unusual three-dimensional structures. These structures include a crisscrossing lattice of two sets of non-parallel 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 studi…
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…
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…
Motivated by the recent theoretical and experimental progress in the heavy fermion system UCoGe, we study ferromagnetic chiral superconductors in the presence of magnetic domains. Within mean field approximations, it is shown that chiral superconducting domains are naturally induced by the ferromagnetic domains. The domain wall current flows in the opposite direction to the naively expected one as in $^3$He-A phase due to contributions from "unpaired electrons". Consequently, the domain wall current flows in the same direction with that of surface currents when the magnetic domain wall lies pa…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state has received renewed interest recently due to the experimental indication of its presence in CeCoIn$_5$, a quasi 2-dimensional (2D) d-wave superconductor. However direct evidence of the spatial variation of the superconducting order parameter, which is the hallmark of the FFLO state, does not yet exist. In this work we explore the possibility of detecting the phase structure of the order parameter directly using conductance spectroscopy through micro-constrictions, which probes the phase sensitive surface Andreev bound states of d-wave supercon…
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 …
We study Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of superconductors with and without inversion symmetry based on the Hubbard model on the square lattice near half-filling, using the random phase approximation. We show that center of mass momentum $Q$ tends to be parallel to $x$- or y-axis in the presence of inversion symmetry, while $Q$ vector is likely to be perpendicular to the magnetic field in the absence of inversion symmetry. We also clarify that $d+f$-wave pairing is favored and the hetero spin triplet $f$-wave state is present in the FFLO state unlike state in the superconductors…
We report high magnetic field linear magnetostriction experiments on CeCoIn$_5$ single crystals. Two features are remarkable: (i) a sharp discontinuity in all the crystallographic axes associated with the upper superconducting critical field $B_{c2}$ that becomes less pronounced as the temperature increases; (ii) a distinctive second order-like feature observed only along the c-axis in the high field (10 T $ \lesssim B \leq B_{c2}$) low temperature ($T \lesssim$ 0.35 K) region. This second order transition is observed only when the magnetic field lies within 20$^o$ of the ab-planes and there i…
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 study the single-plane-wave Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states for BCS--Bose-Einstein condensation (BEC) crossover at general temperatures $T$. Because we include the important effects of noncondensed pairs, our $T \neq 0$ phase diagrams are different from those reported in earlier work. We find that generalized LOFF phases may be the ground state for a wide range of (weak through moderately strong) interactions, including the unitary regime. However, these LOFF phases are readily destroyed by non-zero $T$.
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.
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.
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state can be found in layered d-wave superconductors such as high $T_c$ cuprates and $κ$-(ET)$_2$ salts in a planar magnetic field. We show the superconducting order parameter forms two dimensional crystalline lattice in the FFLO state for d-wave superconductors. Also the quasiparticle density of states and the thermodynamics of FFLO state are constructed. Therefore STM or NMR will provide a definitive test for the existence of the FFLO state.
Spin-polarized attractive Fermi gases in one-dimensional (1D) optical lattices are expected to be remarkably good candidates for the observation of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. We model these systems with an attractive Hubbard model with population imbalance. By means of the density-matrix renormalization-group method we compute the pairing correlations as well as the static spin and charge structure factors in the whole range from weak to strong coupling. We demonstrate that pairing correlations exhibit quasi-long range order and oscillations at the wave number expected …
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…
We study the superconducting order parameter fluctuations near the phase transition into the Larkin-Ovchinnikov-Fulde-Ferrell state in the clean limit at zero temperature. In contrast to the usual normal metal-to-uniform superconductor phase transition, the fluctuation corrections are dominated by the modes with the wave vectors away from the origin. We find that the superconducting fluctuations lead to a divergent spin susceptibility and a breakdown of the Fermi-liquid behavior at the quantum critical point.
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, …
We find theoretically that the vortex core in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is quite different from the ordinary core by a simple topological reason. The intersection point of a vortex and nodal plane of the FFLO state empties the excess spins. This leads to observable consequences in the spatial structure of the spontaneous magnetization. We analyze this topological structure based on the low lying excitation spectrum by solving microscopic Bogoliubov-de Gennes equation to clarify its physical origin.
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…
Measurements of the temperature and angular dependencies of the upper critical fields $H_{c2}$ of a stoichiometric single crystal LiFeAs in pulsed magnetic fields up to 50 T were performed using a tunnel diode resonator. Full $H^{\parallel c}_{c2}(T)$ and $H^{\bot c}_{c2}(T)$ curves with $H^{\parallel c}_{c2}(0)=17 \pm 1$ T, $H^{\bot c}_{c2}(0)=26 \pm 1$ T, and the anisotropy parameter ${γ_H}(T) \equiv H_{c2}^{\bot c}/H_{c2}^{\parallel c}$ decreasing from $\approx 2.5$ at $T_c$ to 1.5 at $T\ll T_c$ were observed. The results for both orientations are in excellent agreement with a theory of $H_…
The crystal structure determines both the Fermi surface and pairing symmetry of the superconducting metals. It is demonstrated in the framework of the general phenomenological approach that this is of the primary importance for the determination of the structure of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in the magnetic field. The FFLO modulation of the superconducting order parameter may be revealed in the form of the higher Landau level states or/and modulation along the magnetic field. The transition between different FFLO states could occur with the temperature variation or with …
We review the properties of two coupled fermionic chains, or ladders, under a magnetic field parallel to the lattice plane. Results are computed by complementary analytical (bosonization) and numerical (density-matrix renormalization group) methods which allows a systematic comparison. Limiting cases such as coupled bands and coupled chains regimes are discussed. We particularly focus on the evolution of the superconducting correlations under increasing field and on the presence of irrational magnetization plateaus. We found the existence of large doping-dependent magnetization plateaus in the…
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…
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…
We develop the Ginzburg-Landau theory of the vortex lattice in clean isotropic three-dimensional superconductors at large Maki parameter, when inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov state is favored. We show that diamagnetic superfluid currents mainly come from paramagnetic interaction of electron spins with local magnetic field, and not from kinetic energy response to the external field as usual. We find that the stable vortex lattice keeps its triangular structure as in usual Abrikosov mixed state, while the internal magnetic field acquires components perpendicular to applied magneti…
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)$_2$…
The heavy-fermion superconductor CeCoIn5 is the first material, where different experimental probes show strong evidence pointing to the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. The inhomogeneous superconducting FFLO state with a periodically modulated order parameter was predicted to appear in Pauli-limited, sufficiently clean type-II superconductors already more than 40 years ago. On the other hand, CeCoIn5 is supposed to be close to a magnetic quantum critical point (QCP) showing strong antiferromagnetic (AFM) spin fluctuations (SF) at atmospheric pressure. We studi…
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 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 …
Due to the difference in the momenta of the superconducting order parameters, the Josephson current in a Josephson junction between a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor and a conventional BCS superconductor is suppressed. We show that the Josephson current may be recovered by applying a magnetic field in the junction. The field strength and direction at which the supercurrent recovery occurs depend upon the momentum and structure of the order parameter in the FFLO state. Thus the Josephson effect provides an unambiguous way to detect the existence of an FFLO state, and to m…
We investigate, mostly analytically, the nature of the Fulde-Ferrell- Larkin-Ovchinnikov superfluid phases for an isotropic two-dimensional superconductor, which is relevant for the experimental observation of these phases. We show that there is, in the low temperature range, a cascade of transitions toward order parameters with ever increasing complexity.
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 find that a model Hamiltonian of s-wave superconductors in the presence of spin-orbit interactions and a Zeeman field is exactly solvable. Most intriguingly, based on the exact solutions, an unconventional type of Fulde-Ferrel-Larkin-Ovchinnikov (FFLO) ground state is rigorously revealed, in which the center-of-mass momentum of the fermion pair is proportional to the Zeeman field. We also elaborate on the drifting effect of the Zeeman field on the spin-orbit-coupled Bose-Einstein condensate.
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 …
Vortex tilt response in Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice is theoretically examined as a probe reflecting the spatial structure of this state. In the FFLO state with nodal planes perpendicular to the magnetic field in a quasi 2D material under a parallel field, the tilt modulus E_{2} {\it of the nodal planes} decreases as the paramagnetic effect is effectively enhanced, and this reduction of E_{2} in turn reduces the vortex tilt modulus. This reduction of vortex tilt modulus, more remarkable in more anisotropic systems, accompanying the FFLO transition may be an origin of …
Motivated by recent NMR data suggesting the presence of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) vortex lattice in magnetic fields perpendicular to the superconducting plane in the heavy-fermion superconductor CeCoIn5, we examine here the stability of FFLO states in quasi two-dimensional (2D) superconductors under a perpendicular field. It is found that a 3D-like portion of Fermi surfaces peculiar to CeCoIn5 stabilizes a FFLO vortex state modulating along the field parallel to the c-axis and that the direction of modulation in a FFLO vortex lattice is related to the characters of the normal t…
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 investigate the vortex state with Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) modulations suggested for a high field phase of CeCoIn_5. On the basis of the quasiclassical Eilenberger theory, we calculate the three dimensional structure of pair potentials, internal magnetic fields, paramagnetic moments, and electronic states, for the s-wave and the d-wave pairings comparatively. The π-phase shift of the pair potential at the FFLO nodal plane or at the vortex core induces sharp peak states in the local density of states, and enhances the local paramagnetic moment. We also discuss the NMR spectrum…
In superconductors with singlet pairing, the inhomogeneous Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is expected to be stabilized by a large Zeeman splitting. We develop an efficient method to evaluate the Landau-Ginzburg free energies of FFLO-state vortex lattices and use it to simplify the considerations that determine the optimal vortex configuration at different points in the phasediagram. We demonstrate that the order parameter spatial profile is completely determined, up to a uniform translation, by its Landau level index n and the vortex Lattice structure and derive an explicit expr…
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.
