FFLO State Research Articles

Angular Fulde–Ferrell–Larkin–Ovchinnikov superfluid due to self-one-dimensionalization in imbalanced cold fermion gases

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 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.

Phase diagram of chiral quark matter: From weakly to strongly coupled Fulde-Ferrell phase

We calculate the phase diagram of two-flavor quark matter within the Nambu-Jona-Lasinio (NJL) model in the temperature-flavor asymmetry plane in the case where there are three competing phases: the homogeneous Bardeen-Cooper-Schrieffer (BCS) phase, the unpaired phase, and a phase with broken spatial symmetry, which is here taken to be the counterpart of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase in condensed matter physics. The system belongs to the universality class of paramagnetic-ferromagnetic-helical systems, and therefore contains a tricritical Lifshitz point in its phase diagram, where the momentum scale characterizing the breaking of translational invariance has a critical exponent of 1/2 to leading order. Upon varying the coupling constant of the theory we find that in weak coupling, the FFLO phase is favored at arbitrary flavor asymmetries for sufficiently low temperatures; at intermediate coupling its occupancy domain is shifted towards larger asymmetries. Strong coupling features a new regime of an inhomogeneous FF state, which we identify with a current-carrying Bose-Einstein condensate of tightly bound up and down quarks. The temperature and asymmetry dependence of the gap function is studied. It is shown that the anomalous temperature dependence of the gap in the homogeneous, flavor-asymmetric phase is transformed into a normal dependence (self-similar to themore » BCS phase) at arbitrary coupling, once the FF phase is allowed for. We analyze the occupation numbers and the Cooper-pair wave function and show that when the condensate momentum is orthogonal to the particle momentum the minority component contains a blocking region (breach) around the Fermi sphere in the weak-coupling limit, which engulfs more low-momentum modes as the coupling is increased, and eventually leads to a topological change in strong coupling, where the minority Fermi sphere contains either two occupied strips or an empty sphere. For nonorthogonal momenta, the blocking region is either reduced or extinct, i.e., no topological changes are observed.« less

25pRK-5 異方的超伝導薄膜におけるゼロ磁場FFLO状態(磁性理論,領域8,強相関系:高温超伝導,強相関f電子系など)

25pRK-5 異方的超伝導薄膜におけるゼロ磁場FFLO状態(磁性理論,領域8,強相関系:高温超伝導,強相関f電子系など)

Signature of the Fulde-Ferrell-Larkin-Ovchinnikov Phase in the Collective Modes of a Trapped Ultracold Fermi Gas

We study theoretically the collective modes of a two-component Fermi gas with attractive interactions in a quasi-one-dimensional harmonic trap. We focus on an imbalanced gas in the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) phase. Using a mean-field theory, we study the response of the ground state to time-dependent potentials. For potentials with short wavelengths, we find dramatic signatures in the large-scale response of the gas which are characteristic of the FFLO phase. This response provides an effective way to detect the FFLO state in experiments.

Superfluid density of the ultra-cold Fermi gas in optical lattices

In this paper, we study the superfluid density of the two-component Fermi gas in optical lattices with population imbalance. Three different types of phases, the BCS state (Bardeen, Cooper and Schrieffer), the FFLO state (Fulde, Ferrel, Larkin and Ovchinnikov) and the Sarma state, are considered. We show that the FFLO superfluid density differs from the BCS/Sarma superfluid density in an important way. Although there are dynamical instabilities in the FFLO phase, when the interaction is strong or densities are high, the FFLO phase is found to be stable on the weak coupling limit.

The Fulde–Ferrell–Larkin–Ovchinnikov phase in the presence of pair hoppinginteraction

The recent experimental support for the presence of the Fulde–Ferrell–Larkin–Ovchinnikov (FFLO)phase in CeCoIn5 directed attention towards the mechanisms responsible for this type of superconductivity.We investigate the FFLO state in a model where on-site/inter-site pairingcoexists with the repulsive pair hopping interaction. The latter interactionis interesting in that it leads to pairing with non-zero momentum of theCooper pairs even in the absence of the external magnetic field (the so-calledη pairing). It turns out that, depending on the strength of the pair hopping interaction, themagnetic field can induce one of two types of the FFLO phase with different spatialmodulations of the order parameter. It is argued that the properties of the FFLO phase maygive information about the magnitude of the pair hopping interaction. We also show thatη pairing and d-wave superconductivity may coexist in the FFLO state. It holds true also forsuperconductors which, in the absence of magnetic field, are of pure d-wave type.

Superconductivity in an almost localized Fermi liquid of quasiparticles with spin-dependent masses and effective-field induced by electron correlations

Paired state of nonstandard quasiparticles is analyzed in detail in two model situations. Namely, we consider the Cooper-pair bound state and the condensed phase of an almost localized Fermi liquid (ALFL) composed of quasiparticles in a narrow-band with the spin-dependent masses (SDM) and an effective field, both introduced earlier and induced by strong electronic correlations. Each of these novel characteristics are calculated in a self-consistent manner. We analyze the bound states as a function of Cooper-pair momentum q in applied magnetic field in the strongly Pauli limiting case (i.e. when the orbital effects of applied magnetic field are disregarded). The spin-direction dependence of the effective mass makes the quasiparticles comprising Cooper pair spin distinguishable in the quantum mechanical sense, whereas the condensed gas of pairs may still be regarded as composed of identical entities. The Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) condensed phase of moving pairs is by far more robust in the applied field for the case with spin-dependent masses than in the situation with equal masses of quasiparticles. Relative stability of the Bardeen-Cooper-Schrieffer (BCS) vs. FFLO phase is analyzed in detail on temperature - applied field plane. Although our calculations are carried out for a model situation, we can conclude that the spin-dependent masses should play an important role in stabilizing high-field low-temperature (HFLT) unconventional superconducting phases (FFLO being an instance) in systems such as CeCoIn_5, organic metals, and possibly others.

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

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

The disordered Fulde–Ferrel–Larkin–Ovchinnikov state in d-wave superconductors

We study the Fulde–Ferrel–Larkin–Ovchinnikov (FFLO) superconducting state in 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–de Gennes (BdG) equation. The spatial structure of the modulated superconducting order parameter and the magnetic properties in the disordered FFLO state are investigated. We point out the possibility of the ‘FFLO glass’ state in the presence of strong point disorders, which arises from the configurational degree of freedom of the FFLO nodal plane. The distribution function of the local spin susceptibility is calculated and its relationship with the FFLO nodal plane is clarified. We discuss the nuclear magnetic resonance (NMR) measurements for CeCoIn5.

Quantum polarization spectroscopy of correlations in attractive fermionic gases

We show how spin–spin correlations, detected in a non-destructive way via spatially resolved quantum polarization spectroscopy, strongly characterize various phases realized in trapped ultracold fermionic atoms. Polarization degrees of freedom of the light couple to spatially resolved components of the atomic spin. In this way, quantum fluctuations of matter are faithfully mapped onto those of light. In particular, we demonstrate that quantum spin polarization spectroscopy provides a direct method to detect the Fulde–Ferrell–Larkin–Ovchinnikov phase realized in a one-dimensional imbalanced Fermi system.

π Phase Superconductivity and Magnetism in Ferromagnet / Superconductor / Ferromagnet Trilayers

On the base of new boundary-value problem for the Eilenberger function we investigate the superconducting and magnetic states in ferromagnet/superconductor (FM/S) nanostructures, where superconductivity is a superposition of the BCS pairing with zero total momentum in the S layers and the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) pairing with nonzero 3D coherent momentum k in the FM layers. We originally study the interplay between the BCS and FFLO states in the pure thin FM/S/FM trilayers and two novel -phase superconducting states with electron-electron repulsion in the FM layers are predicted. The modulated FFLO states are possible in such trilayers only in presence of external magnetic field at suitable parameters of the FM and S layers. In the FM/S superlattices there are also two -phase magnetic states (0 and ) with compensation of the exchange field paramagnetic effect. This fact allows us to explain a surprisingly high Tc ~ 5K in the short period Gd/La superlattice and to predict the sign and value of the electron-electron interaction in the ferromagnetic Gd metal.

Proximity Effect as a Probe of Electronic Correlations and Exchange Field in Dirty Ferromagnet/Superconductor Nanostructures

We investigate the interplay between the BCS and 2D Larkin-Ovchinnikov-Fulde-Ferrell (LOFF) states in the dirty thin ferromagnetic metal/superconductor (FM/S) nanostructures. For the FM/S bilayers we have derived the dependencies of critical temperature on the FM layer exchange field, electronic correlations and thickness. Moreover, in the corresponding FM/S/FM trilayers we predict two new π phase superconducting states with electron-electron repulsion in the FM layers. The 2D modulated LOFF states are possible in such trilayers only in presence of a weak magnetic field and at suitable parameters of the FM and S layers. On this base we originally propose the method of proximity effect probe the magnitude and sign of the electronic correlations, the order parameter symmetry and exchange fields in various FM layers.

Competition between triplet, singlet and FFLO states in organic superconductors (TMTSF)2X under magnetic field

We study the competition between triplet f-wave, singlet d-wave, and the FFLO state in a model for (TMTSF)2X using random phase approximation. The result suggests the possibility of the singlet→FFLO→triplet transition upon increasing the magnetic field. We also show that the triplet component mixing increases in the FFLO state with increasing the magnetic field, and the off-site repulsions increase the mixing rate. The results seem to suggest that the large triplet mixing results in an enhanced tendency toward the FFLO state over the usual pairing state.

Antiferromagnetic order in the FFLO state

We investigate the antiferromagnetic (AF) order in the d-wave superconducting (SC) state at high magnetic fields. A two-dimensional model with on-site repulsion U, inter-site attractive interaction V and antiferromagnetic exchange interaction J is solved using mean field theory. For finite values of U and J, a first order transition occurs from the normal state to the FFLO state, while the FFLO-BCS phase transition is second order, consistent with the experimental results in CeCoIn5. Although the BCS-FFLO transition is continuous, the Neél temperature of AF order is discontinuous at the phase boundary because the AF order in the FFLO state is induced by the Andreev bound state localized in the zeros of FFLO order parameter, while the AF order hardly occurs in the uniform BCS state. The spatial structure of the magnetic moment is investigated for the commensurate AF state as well as for the incommensurate AF state. The influence of the spin fluctuations is discussed for both states. Since the fluctuations are enhanced in the normal state for incommensurate AF order, this AF order can be confined in the FFLO state. The experimental results in CeCoIn5 are discussed.

Superconducting fluctuations near the FFLO state

The Fulde, Ferrell, Larkin & Ovchinnikov (FFLO) state consists in a modulation of the superconducting order parameter due to Zeeman effect. In a Ginzburg-Landau approach, higher order terms than usual in the gradient expansion, i.e. quartic terms, are needed to take into account the FFLO modulation. The role of this quartic term in addition to the quadratic usual term in a Gaussian fluctuation spectrum have been investigated for heat capacity C and paraconductivity s near a FFLO state for both isotropic and anisotropic cases. In the isotropic (resp. anisotropic) case, the power laws are drastically different (resp. similar) in comparison with the homogeneous superconductivity case. Nevertheless, for the anisotropic case the anisotropic ratio δxx/δyy is quite different for a FFLO phase than for a BCS one. In addition, we predict anomalous power laws near the tricritical point where the normal phase and the two superconducting (uniform and FFLO) phases are merging. The multiple crossovers associated with the phase transitions between homogeneous, tricritical and inhomogenous fluctuation regimes thus may serve as a powerful tool to identify the FFLO phases.

Field-induced dimensional crossover and anomalous superconducting states in the quasi-one-dimensional superconductor (TMTSF)2C1O4

Quasi-one-dimensional (Q1D) superconductivity becomes stable in high magnetic fields due to the field-induced dimensional crossover (FIDO) and a stabilization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) states. We have studied the field-direction and field-amplitude dependence of the onset temperature Tonsetc of the superconducting state of the organic superconductor (TMTSF)2C1O4. Comparing the in-plane field-angle ϕ dependence of Tonsetc and the behavjor of the inter-plane resistance, we show that the FIDO stabilizes the superconductivity when the field is more than 19° away from the a axis. In addition, we demonstrate that Tonset remains finite for H || a up to H = 50 kOe, as well as for H || b. The high-field states are anomalous in nature, suggesting that different FFLO states are realized.

Discontinuous superconducting transitions in the paramagnetic limit: a non-perturbative approach

The unusual superconducting (SC) phase transitions occuring under competing orbital and spin pair breaking, which characterize clean strongly type-II superconductors at low temperatures, are investigated within a non-perturbative approach, which avoides the difficulties encountered in various perturbative approaches and enables comparison with recent experimental data. It is shown that in a 3D system with strong spin-splitting, a spatial (FFLO) modulation of the order parameter along the magnetic-field direction preserves the continuous nature of the SC transition. However, at a magnetic field slightly below Hc2 the FFLO state becomes unstable, transforming discontinuously into a uniform SC state via a first-order phase transition. Our calculation shows that the entropy jump at the first-order phase transition is siginificantly larger than its total variation in the continuous region between the two transitions, in agreement with recent thermal-conductivity measurements performed on the heavy-fermion compound URu2Si2.

Pressure induced FFLO instability in multi-band superconductors

Multi-band systems such as inter-metallic and heavy fermion compounds havequasi-particles arising from different orbitals at their Fermi surface. Since thesequasi-particles have different masses or densities, there is a natural mismatch of the Fermiwavevectors associated with different orbitals. This makes these materials potentialcandidates to observe exotic superconducting phases as Sarma or FFLO phases, even in theabsence of an external magnetic field. The distinct orbitals coexisting at the Fermi surfaceare generally hybridized and their degree of mixing can be controlled by external pressure.In this work we investigate the existence of an FFLO type of phase in a two-band BCSsuperconductor controlled by hybridization. At zero temperature, as hybridization(pressure) increases we find that the BCS state becomes unstable with respect toan inhomogeneous superconducting state characterized by a single wavevectorq.

Exploring exotic superfluidity of polarized ultracold fermions in optical lattices

Superfluidity with imbalanced populations of harmonically trapped ultracold fermions in a two-dimensional optical lattice is investigated by solving the Bogoliubov-de Gennes equations. The intriguing richness of patterns between competing ferromagnetic and superfluid phases for different filling densities has been revealed. At low density, the main experimental features could be reproduced, especially the bimodal distribution of ferromagnetism. The superfluid-pairing gap oscillates radially, demonstrating the realization of the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state. In the high-density regime, another type of FFLO state with gap oscillation along the angular direction shows up and the accompanying ferromagnetic order modulates accordingly. The square lattice like FFLO state may appear at the intermediate densities. Moreover, we suggest other experimental proposals of observing the unique FFLO features straightforwardly.

Types of Fulde-Ferrell-Larkin-Ovchinnikov states induced by anisotropy effects

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 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 the magnetic field rotation.