Novel dynamical excitations and roton-based measurement of Cooper-pair momentum in a two-dimensional Fulde-Ferrell-Larkin-Ovchinnikov superfluid on optical lattices
Key Laboratory for Microstructural Material Physics of Hebei Province, School of Science, Yanshan University（河北工业大学微观结构物理重点实验室，理学院，燕山大学）；Centre for Theoretical and Computational Physics, College of Physics, Qingdao University（青岛大学物理学院理论计算物理中心）；School of Physics and Astronomy, Beijing Normal University（北京师范大学物理与天文学院）
Shuning Tan, Jiayi Shi, Peng Zou, Tianxing Ma, Huaisong Zhao
Determining the center-of-mass (COM) momentum of Cooper pairs in unconventional superconductors or superfluids is a topic of great interest in condensed matter physics and ultracold atomic gases. Theoretically, we investigate the dynamical excitations of a two-dimensional spin-polarized attractive Hubbard model on a square optical lattice under an effective Zeeman field by computing the density and spin dynamical structure factors, focusing on phase transition from a Bardeen-Cooper-Schrieffer (BCS) superfluid to an Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid. In the FFLO superfluid, besides the phonon mode in the density channel, a low-energy bogolon mode emerges in the spin channel, which is associated with Bogoliubov quasiparticles on a Bogoliubov Fermi surface. Moreover, the dynamical excitations exhibit pronounced anisotropy in momentum space due to the finite COM momentum. At half filling, the roton mode around $[π,π]$ evolves from a point-like minimum into a ring structure shifted by the COM momentum across the BCS-FFLO transition, providing a roton-based protocol to extract the COM momentum. These predictions provide key insights for confirming the existence of FFLO superfluids and understanding their dynamical excitation spectra.
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.
We study an effect of rotation on the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state of two component Fermi superfluid gases in a toroidal trap. We investigate a stability of the FFLO states in the quasi-one-dimensional regime on the basis of the Bogoliubov-de Gennes equation. We find that two novel FFLO phases, i.e., the half quantum vortex state and the intermediate state of Fulde-Ferrell (FF) state and Larkin-Ovchinnikov (LO) state, are stabilized by the rotation. The phase diagram for the FF state, LO state, intermediate state, and half quantum vortex state is shown in both T-P plane and T-…
Superconductor with a spatially-modulated order parameter is known as Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superconductor. Using the time-dependent Ginzburg-Landau (TDGL) formalism we have theoretically studied the temporal behaviour of the equal-time correlation function, or the structure factor, of a FFLO superconductor following a sudden quench from the unpaired, or normal, state to the FFLO state. We find that quenching into the ordered FFLO phase can reveal the existence of a line in the mean-field phase diagram which cannot be accessed by static properties.
We present the study of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing states in the $p$-orbital bands in both two and three-dimensional optical lattices. Due to the quasi one-dimensional band structure which arises from the unidirectional hopping of the orthogonal $p$-orbitals, the pairing phase space is not affected by spin imbalance. Furthermore, interactions build up high dimensional phase coherence which stabilizes the FFLO states in 2D and 3D optical lattices in a large parameter regime in phase diagram. These FFLO phases are stable with imposing the inhomogeneous trapping potential…
We calculate the pair susceptibility of an attractive spin-polarized Fermi gas in the normal phase, as a function of the pair momentum. Close to unitarity, we find a strong enhancement of Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing fluctuations over an extended region of the temperature-polarization phase diagram, which manifests itself as a pronounced peak in the pair-momentum distribution at a finite pair momentum. This peak should be amenable to experimental observation at achievable temperatures in a box-like trapping potential, as a fingerprint of FFLO pairing. Our calculations rest o…
We propose a two-step experimental protocol to directly engineer Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a cold two-component Fermi gas loaded into a quasi-one-dimensional trap. First, one uses phase imprinting to create a train of domain walls in a superfluid with equal number of $\uparrow$- and $\downarrow$-spins. Second, one applies a radio-frequency sweep to selectively break Cooper pairs near the domain walls and transfer the $\uparrow$-spins to a third spin state which does not interact with the $\uparrow$- and $\downarrow$-spins. The resulting FFLO state has exactly one unpair…
Based on the matrix product states method, we investigate numerically the ground state properties of one-dimensional mixtures of repulsive bosons and spin-imbalanced attractive fermions, the latter being in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state, where Cooper pairs condense at a finite momentum $k=k_{FFLO}$. We find that the visibility of such a state is dramatically enhanced as the repulsive Bose-Fermi mixture is brought close to the phase-separation point. In particular, large amplitude self-induced oscillations with wave-vector $2k_{FFLO}$ appear in both the fermion total density…
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.
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.
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.
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…
The topological superfluids with Majorana zero modes have not yet been realized in ultracold atoms with Rashba spin-orbit coupling. Here we show that these phases can be realized with an artificial gauge potential, which can be regarded as a site-dependent rotating Zeeman field. This potential breaks the inversion symmetry and plays the same role as Rashba spin-orbit coupling. In the inverted bands, this model can open a proper parameter regime for topological superfluids. Strikingly, we find that the interaction near the Fermi surface is dominated by the dispersion scattering in the same band…
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 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.
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…
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 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.
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 …
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 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 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 propose that in a system with pocket Fermi surfaces, a pairing state with a finite total momentum q_tot like the Fulde-Ferrell-Larkin-Ovchinnikov state can be stabilized even without a magnetic field. When a pair is composed of electrons on a pocket Fermi surface whose center is not located at Gamma point, the pair inevitably has finite q_tot. To investigate this possibility, we consider a two-orbital model on a square lattice that can realize pocket Fermi surfaces and we apply fluctuation exchange approximation. Then, by changing the electron number n per site, we indeed find that such sup…
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 …
Clean superconductors with weakly coupled conducting planes have been suggested as promising candidates for observing the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. We consider here a layered superconductor in a magnetic field of arbitrary orientation with respect to the conducting plane. In this case there is competition of spin-pair-breaking and orbital-pair-breaking effects. In previous work, phase boundaries characterized by Landau quantum numbers n > 0 have been predicted. Here, we calculate the actual structure of the stable states below Hc2 by minimizing the free energy. We find sev…
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…
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…
We measure the heat capacity of UBe13 with an unusually low Tc for a polycrystal. We find an upturn in the upper critical field Hc2(T) below about Tc/2, much as for higher-Tc samples. Comparing the critical fields in our sample and in samples with higher Tc's shows that the low-temperature limit of Hc2 is proportional to Tc(H=0), as expected if the upturn comes from an FFLO phase and strong coupling.
We consider a formation of the Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) phase in a quasi-one-dimensional (Q1D) conductor in a magnetic field, parallel to its conducting chains, where we take into account both the paramagnetic spin-splitting and orbital destructive effects against superconductivity. We show that, due to a relative weakness of the orbital effects in a Q1D case, the LOFF phase appears in (TMTSF)$_2$ClO$_4$ superconductor for real values of its Q1D band parameters. We compare our theoretical calculations with the recent experimental data by Y. Maeno's group [S. Yonezawa et al., Phy…
We study exotic superconducting states in SrTiO$_3$ heterostructures on the basis of the three-orbital model, which reproduces the band structure of two-dimensional electron gases. We show various Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states induced by the broken inversion symmetry and orbital degree of freedom. In particular, a novel orbital-dependent FFLO state is stabilized in a magnetic field along the [110]-axis. The field angle dependence of the FFLO state is clarified on the basis of the spin and orbital texture in the momentum space. It is shown that the orbital degree of freedom in …
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state is a superconducting state stabilized by a large Zeeman splitting between up- and down-spin electrons in a singlet superconductor. In the absence of disorder, the superconducting order parameter has a periodic spatial structure, with periodicity determined by the Zeeman splitting. Using the Bogoliubov-de Gennes (BdG) approach, we investigate the spatial profiles of the order parameters of FFLO states in a two-dimensional s-wave superconductors with nonmagnetic impurities. The FFLO state is found to survive under moderate disorder strength, and …
The effect of a nonmagnetic impurity on the subgap electronic spectrum in a d-wave superconductor in the Fulde-Ferrell-Larkin-Ovchinnikov state is investigated. In a pure system, the spatial variation of the order parameter (OP) of the FFLO state forms a two-dimensional lattice, and there exist two types of sub-gap quasi-particle states. Our numerical iterations indicate that an OP saddle point, and slightly less so energetically, an OP extremum favor to be pinned at the impurity site. The local density of states and the fixed-bias map reveal the subtle effects of an impurity on the subgap ene…
The effect of impurities on Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states in a layered superconductor with d-wave pairing symmetry is investigated using the tight-binding model and the Bogoliubov-de Gennes equations. At low temperature and a strong exchange field applied parallel to its conducting plane, a two-dimensional (2D) square lattice-like Larkin-Ovchinnikov state is more energetically favorable in a clean system. In the presence of impurities, the spatial profile of the order parameter remains as a 2D square lattice, and it is distorted only near the impurities when the impurity conce…
The possibility of a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state in a population imbalanced Fermi gas with a vortex is proposed. Employing the Bogoliubov-de-Gennes formalism we self-consistently determine the superfluid order parameter and the particle number density in the presence of a vortex. We find that as increasing population imbalance, the superfluid order parameter spatially oscillates around the vortex core in the radial direction, indicating that the FFLO state becomes stable. We find that the radial FFLO states cover a wide region of the phase diagram in the weak-coupling regime …
We study theoretically two spatially separate quasi-one-dimensional atomic Fermi gases in a double-well trap. By tuning independently their spin polarizations, a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid or a Bardeen-Cooper-Schrieffer (BCS) superfluid may be formed in each well. We seek the possibility of creating a spatially tunable atomic Josephson junction between two superfluids, which is supposed to be realizable via building a weak link at given positions of the double-well barrier. We show that within mean-field theory the maximum Josephson current is proportional to the order …
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…
Angular dependent magnetothermal conductivity experiments on CeCoIn_5 indicate that this compound is a d-wave superconductor. In this study, the low-temperature behavior of the upper critical field is measured in a single crystal of CeCoIn_5 along the directions H parallel a and H parallel c. The data is compared with model calculations of the upper critical field in a d-wave superconductor. It is found that the observed H_c2(T) along H parallel a is consistent with a Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state at low temperatures, T < 0.7K, whereas for H parallel c the FFLO state appears to…
We solve a long-standing problem about a theoretical description of the upper critical magnetic field, parallel to conducting layers and perpendicular to conducting chains, in (TMTSF)$_2$ClO$_4$ superconductor. In particular, we explain why the experimental upper critical field, $H^{b'}_{c2} \simeq 6 \ T$, is higher than both the quasi-classical upper critical field and Clogston paramagnetic limit. We show that this property is due to the coexistence of the hidden Reentrant and Larkin-Ovchinnikov-Fulde-Ferrell phases in a magnetic field in a form of three plane waves with non-zero momenta of t…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase was first predicted in 2D superconductors about 50 years ago, but so far unambiguous experimental evidences are still lacked. The recently experimentally realized spin-imbalanced Fermi gases may potentially unveil this elusive state, but require very stringent experimental conditions. In this Letter, we show that FFLO phases may be observed even in a 3D degenerate Fermi gas with spin-orbit coupling and in-plane Zeeman field. The FFLO phase is driven by the interplay between asymmetry of Fermi surface and superfluid order, instead of the interpl…
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 th…
The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states for two-dimensional s- and d-wave superconductors (s- and d-SC) are self-consistently studied under an in-plane magnetic field. While the stripe solution of the order parameter (OP) is found to have lower free energy in s-SC, a square lattice solution appears to be energetically more favorable in the case of d-SC. 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-SC exhibit bias-energy-dependent checkerboard patterns. T…
Effect of the phase fluctuations of the order parameter on the stability of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states are examined in exactly two-dimensional (2D) type-II superconductors with cylindrically symmetric Fermi surface on the basis of a generalized Ginzburg-Landau theory. It is found that for the FFLO states with oscillations in a single direction, not only the long-range order but also quasi-long-range order (QLRO), which is characterized by a power law decay of the order parameter correlation function, is suppressed by the phase fluctuations at any finite temperatures. On…
