Superfluid Fermi Liquid Research Articles

Origins of anomalies in the temperature dependences of specific heat and superfluid density in doped high-Tc cuprates: Signatures of Bose-liquid superconductivity

We show that the temperature-dependent superconducting order parameter and related superconducting properties (in particular, the temperature dependences of specific heat, superfluid density and related London penetration depth) of high-[Formula: see text] cuprates are fundamentally different from those of conventional superconductors and cannot be understood within the existing theories based on the Bardeen–Cooper–Schrieffer (BCS)-type condensation of weakly bound Cooper pairs into a superfluid Fermi-liquid and on the usual Bose–Einstein condensation (BEC) of bosonic Cooper pairs. We examine the validity of an alternative approach to the unconventional superconductivity in high-[Formula: see text] cuprates and establish that these materials exhibiting a [Formula: see text]-like superconducting transition at the critical temperature [Formula: see text] are similar to the superfluid 4He and are also superfluid Bose systems. We argue that the doped high-[Formula: see text] cuprates, from underdoped to overdoped regime, are unconventional (bosonic) superconductors and the tightly bound (polaronic) Cooper pairs in these polar materials behave like composite bosons just like 4He atoms and condense into a Bose superfluid at [Formula: see text]. We identify the superconducting order parameter [Formula: see text] in underdoped and optimally doped cuprates as the coherence parameter [Formula: see text] of bosonic Cooper pairs, which appears just below [Formula: see text] and has a kink-like temperature dependence near the characteristic temperature [Formula: see text]. We find that the [Formula: see text]-like specific heat anomaly in high-[Formula: see text] cuprates near [Formula: see text] predicted by the theory of Bose-liquid superconductivity is similar to that observed both in superfluid 4He near [Formula: see text] and in Hg-based cuprate superconductor HgBa2Ca2Cu3O8 near [Formula: see text][Formula: see text]K. We demonstrate that in high-[Formula: see text] superconductor YBa2Cu3[Formula: see text] the superfluid density [Formula: see text] exhibits distinctly different temperature dependences in the temperature ranges [Formula: see text] and [Formula: see text]. In this superconductor, a pronounced anomaly in [Formula: see text] exists near [Formula: see text] and the temperature dependence of [Formula: see text] below [Formula: see text] deviates downwards from the high-temperature behavior. Our results for the normalized superfluid density [Formula: see text] are in good agreement with the experimental data on the temperature dependence of [Formula: see text] in YBa2Cu3[Formula: see text]. The anomalous temperature dependences of specific heat and superfluid density observed in Hg- and Y-based high-[Formula: see text] superconductors are clear signatures of Bose-liquid superconductivity.

Critical end point and universality class of neutron P23 superfluids in neutron stars

We study the thermodynamics and critical behavior of neutron $^3P_2$ superfluids in the inner cores of neutron stars. $^3P_2$ superfluids offer a rich phase diagram including uniaxial/biaxial nematic phases, the ferromagnetic phase, and the cyclic phase. Using the Bogoliubov-de Gennes (BdG) equation as superfluid Fermi liquid theory, we show that a strong (weak) magnetic field drives the first (second) order transition from the dihedral-two biaxial nematic phase to dihedral-four biaxial nematic phase in low (high) temperatures, and their phase boundaries are divided by the critical endpoint (CEP). We demonstrate that the set of critical exponents at the CEP satisfies the Rushbrooke, Griffiths, and Widom equalities, indicating a new universality class. At the CEP, the $^3P_2$ superfluid exhibits critical behavior with nontrivial critical exponents, indicating a new universality class. Furthermore, we find that the Ginzburg-Landau (GL) equation up to the 8th-order expansion satisfies three equalities and properly captures the physics of the CEP. This implies that the GL theory can provide a tractable way for understanding critical phenomena which may be realized in the dense core of realistic magnetars.

Hydrodynamics and proper vibrations of quantum liquids with conformational degrees of freedom

The order parameters are constructed for a Fermi liquid with conformational degrees of freedom. Based on them, additional thermodynamic parameters were introduced: the spin unit vector dα (determining the anisotropy in the spin subspace), the unit spatial vectors mi and ni (determining the anisotropy in space), and also three scalar parameters determining the shape of the Cooper pair u, v, q ( first two items are half-axes of ellipsoid of Cooper pair and last item is mutual orientation in space of these half axes). The symmetry properties of the order parameter operator are considered. The equations of ideal hydrodynamics of a Fermi liquid are derived taking into account the influence of conformational degrees of freedom. By conformational degrees of freedom should be understood the parameters associated with the shape and size of the Cooper pair. Expressions are obtained for the flows of thermodynamic quantities of such a Fermi liquid in terms of the density of the energy functional. The energy functional depends both on the additive integrals of motion (classical fluid parameters) and on conformational parameters. The dispersion equation of such a liquid is obtained for a model representation of the energy functional (the work was performed as part of the Fermi-liquid approach). The dispersion equation includes spin modes, first, second, and third sounds. The dispersion equation for the spatial subsystem, including the first, second, and third sounds characteristic of superfluid systems, is analyzed. Particular solutions of the dispersion equation are simulated using the Maple software package (several 3D figures are given for the angular dependence of the speeds of 1 and 2 sounds in a spherical coordinate system). All of the above allows us to conclude that such a Fermi liquid can be considered as a superfluid liquid crystal of a nematic type. The presence of conformational parameters distinguishes the considered phase from the F phase of a superfluid Fermi liquid.

Analytical derivation of expressions for the specific heat of superfluid Fermi liquids with anisotropic spin-triplet p-wave pairing at finite temperatures

Analytical expressions for the specific heat of superfluid Fermi liquids (SFLs) with anisotropic spin-triplet p-wave pairing of the 3He-A type have been obtained based on a generalised Fermi-liquid approach both at the low temperatures of 0 < T ≪Tc0 (n) and near the temperature of the phase transition [Tc0 (n)] from a normal to a superfluid phase in the absence of a magnetic field. Apart from liquid 3He-A, we also study dense superfluid neutron matter (SNM) with anisotropic spin-triplet p-wave pairing (similar to 3He-A) at subnuclear (n < n0, where n0 = 0.17 fm–3 is the nuclear density) and supernuclear densities (n > n0) in view of generalised Skyrme forces (with additional terms depending on the density n). At 0 < T ≪Tc0 (n), we have obtained an asymptotic expansion for the specific heat CSNM(SFL)(T,n), in which, apart from the main term ∼ T 3 (known for 3He-A in the limit of T → 0) there is an additional correction term (∼ T5), which may reach several percent of the contribution from the main term to the decomposition of the specific heat of SNM (or SFLs). An analytical formula has also been derived for calculating the specific heat CSNM(SFL)(T,n) at temperatures near Tc0(n). The expressions obtained for the CSNM(T,n) functions (valid for an arbitrary parametrisation of the effective Skyrme interaction in neutron matter) have been defined for SNM with the generalised BSk21 parametrisation of Skyrme forces. In addition, dependency graphs were plotted for the specific heat CBSk21(t, y) in the reduced temperature range of 0 < t ≡ T/Tc0(n) ≪ 1 and at t ≲ 1 for dense SNM (at 0.1 ≤ y ≡ n/n0 ≤ 1.7). These results may be of interest for neutron star physics in connection with neutron star cooling (in the presence of neutron superfluidity with anisotropic spin-triplet p-wave Cooper pairing in the outer part of dense liquid neutron star cores).

P23superfluids are topological

We clarify topology of $^3P_2$ superfluids which are expected to be realized in the inner cores of neutron stars and cubic odd-parity superconductors. $^3P_2$ phases include uniaxial/biaxial nematic phases and nonunitary ferromagnetic and cyclic phases. We here show that all the phases are accompanied by different types of topologically protected gapless fermions: Surface Majorana fermions in nematic phases and a quartet of (single) itinerant Majorana fermions in the cyclic (ferromagnetic) phase. Using the superfluid Fermi liquid theory, we also demonstrate that dihedral-two and -four biaxial nematic phases are thermodynamically favored in the weak coupling limit under a magnetic field. It is shown that the tricritical point exists on the phase boundary between these two phases and may be realized in the core of realistic magnetars. We unveil the intertwining of symmetry and topology behind mass acquisition of surface Majorana fermions in nematic phases.

Pairbreaking effect of correlated impurities in a superfluid Fermi liquid

The conventional theory of superconducting alloys does not take into account the discrete character of impurities. Experimental data for superfluid 3He in aerogel and for some high-Tc superconductors reveal a significant discrepancy between the observed temperatures, Tc, of their transitions in the superfluid or superconducting states and those predicted theoretically. Here a theoretical scheme is presented for finding corrections to the Tc originating from spatial correlations between impurities. Analysis is limited to the Ginzburg and Landau temperature region. The shift of Tc with respect to the pure material is represented as a series in concentration of the impurities, x. In the first order on x, the conventional mean-field result for lowering Tc is recovered. The contribution of correlations enters the second-order term. It is expressed via the structure factor of the ensemble of impurities. For superfluid 3He in a silica aerogel, the sign of the correction corresponds to an enhancement of the Tc, so that the resulting pair-breaking effect of impurities is weakened. When the correlation radius of the impurities, R, exceeds the coherence length of the superfluid, the contribution of correlations to the shift of Tc acquires a factor, and the weakening of the pair-breaking effect becomes appreciable. The presented scheme is applied to the superfluid 3He in aerogel.

Transverse force on a vortex and vortex mass: Effects of free bulk and vortex-core bound quasiparticles

The paper reassesses the old but still controversial problem of the transverse force on a vortex and the vortex mass. The transverse force from free bulk quasiparticles on the vortex, both in the Bose and the Fermi liquid, originates from the Aharonov--Bohm effect. However, in the Fermi liquid one should take into account peculiarities of the Aharonov--Bohm effect for BCS quasiparticles described by two-component spinor wave functions. There is no connection between the transverse force (either from free bulk quasiparticles or from vortex-core bound quasiparticles) and the spectral flow in the vortex core in superfluid Fermi liquid, in contrast to widely known claims. In fact, there is no steady spectral flow in the core of the moving vortex, and the analogy with the Andreev bound states in the SNS junction, where the spectral flow is really possible, is not valid in this respect. The role of the backflow on the vortex mass is clarified. The backflow is an inevitable consequence of a mismatch between the currents inside and outside the vortex core and restores the conservation of the particle number (charge) violated by this mismatch. In the Fermi liquid the backflow compensates the current through the core bound states, which is a source of the vortex mass (the Kopnin mass). This results in renormalization of the Kopnin vortex mass by a numerical factor.

Spin excitonic and diffusive modes in superfluid Fermi liquids

The role of the particle-particle $p$-wave spin interaction in Fermi liquids with an $s$-wave pairing is studied. Depending on the sign of the interaction, there arises either a new exciton collective mode below the pair-breaking threshold or a diffusive excitation mode above the threshold. The Landau parameters that control the interaction strength are evaluated for various systems: dilute fermion gases, a degenerate electron liquid, metals, atomic nuclei, and neutron matter. The interaction removes also the square-root singularity in the phase space of pair-breaking processes. How these effects influence the neutrino emissivity in neutron Cooper-pair recombinations in neutron stars is shown.

Superfluid nucleon matter in and out of equilibrium and weak interactions

The Larkin-Migdal approach to a cold superfluid Fermi liquid is generalized for a non-equilibrium system. The Schwinger-Keldysh diagram technique is applied. The developed formalism is applicable to the pairing in the states with arbitrary angular momenta. We consider the white body radiation problem by calculating probabilities of different direct reactions from a piece of a fermion superfluid. The closed diagram technique is formulated in terms of the full Green's functions for systems with the pairing correlation. The cutting rules are used to classify the diagrams representing one-nucleon, two-nucleon, etc. processes in the matter. The important role of multi-piece diagrams for the vector-current conservation is demonstrated. In the case of equilibrated systems, dealing with dressed Green's functions, we demonstrate correspondence between calculations in the Schwinger-Kadanoff-Baym-Keldysh formalism and the ordinary Matsubara technique. As an example we consider neutrino radiation from the neutron pair breaking and formation processes in case of a singlet pairing. Necessary correlation effects are included. The in-medium renormalization of normal and anomalous vertices is performed.

Hamiltonian formulation of the effective kinetic theory for superfluid Fermi liquids

We present in a local form the time dependent effective description of a superfluid Fermi liquid which includes Landau damping effects at T≠0. This is achieved by the introduction of an additional variable, the quasiparticle distribution function, which obeys a simple kinetic equation. The transport equation is coupled with first order equations for the Goldstone mode and the particle density. We prove that a main feature of this formulation is its Hamiltonian structure relative to a certain Poisson bracket. We construct the Hamiltonian to quadratic order.

Neutral weak currents in nucleon superfluid Fermi liquids: Larkin-Migdal and Leggett approaches

Neutrino emission in the processes of breaking and formation of nucleon Cooper pairs is calculated in the framework of the Larkin-Migdal and Leggett approaches to the description of superfluid Fermi liquids at finite temperatures. We explain peculiarities of both approaches and explicitly demonstrate that they lead to the same expression for the emissivity in pair breaking and formation processes.

Superfluid response and the neutrino emissivity of baryon matter: Fermi-liquid effects

The linear response of a nonrelativistic superfluid baryon system on an external weak field is investigated while taking into account the Fermi-liquid interactions. We generalize the theory developed by Leggett for a superfluid Fermi-liquid at finite temperature to the case of time-like momentum transfer typical of the problem of neutrino emission from neutron stars. A space-like kinematics is also analyzed for completeness and compared with known results. We use the obtained response functions to derive the neutrino energy losses caused by recombination of broken pairs in the electrically neutral superfluid baryon matter. We find that the dominant neutrino radiation occurs through the axial-vector neutral currents. The emissivity is found to be of the same order as in the BCS approximation, but the details of its temperature dependence are modified by the Fermi-liquid interactions. The role of electromagnetic correlations in the pairing case of protons interacting with the electron background is discussed in the conclusion.

Superfluid Fermi liquid in a unitary regime

A short popular review of theoretical and experimental results about properties of ultracold Fermi gases in vicinity of the Feshbach resonance is presented. The paper is based on the authors talk on the meeting of the Physical Department of the Russian Academy of Sciences dedicated to 100th anniversary of the birth of L. D. Landau (Moscow, January 22, 2008). A version of this article has been published in Physics - Uspekhi v. 51 p. 603 (2008).

Neutrino emission due to Cooper-pair recombination in neutron stars reexamined

Neutrino emission in processes of breaking and formation of neutron and proton Cooper pairs is calculated within the Larkin-Migdal-Leggett approach for a superfluid Fermi liquid. We demonstrate explicitly that the Fermi-liquid renormalization respects the Ward identity and ensures the weak vector-current conservation. The systematic expansion of the emissivities for small temperatures and nucleon Fermi velocity ${v}_{\mathrm{F},i},i=n,p,$ is performed. Both neutron and proton processes are mainly controlled by the axial-vector current contributions, which are not strongly changed in the superfluid matter. Thus, compared to earlier calculations, the total emissivity of processes on neutrons paired in the $1{S}_{0}$ state is suppressed by a factor of $\ensuremath{\simeq}(0.9\text{\ensuremath{-}}1.2){v}_{\mathrm{F},n}^{2}$. A similar suppression factor ($~{v}_{\mathrm{F},p}^{2}$) arises for processes on protons.

Microscopic theory of sound propagation in the superfluidHe3–aerogel system

We present a theory of sound propagation in superfluid $^{3}\mathrm{He}$ confined in aerogel, taking dragged aerogel motion into account. The superfluid dynamics coupled with the aerogel motion is formulated by use of the Keldysh Green's function for weak-coupling superfluid Fermi liquid. We apply the theory to the hydrodynamic regime and calculate the attenuation of a hydrodynamic longitudinal sound mode, the so-called fast mode. The result is compared to the acoustic experiment reported by the Northwestern University group [R. Nomura, G. Gervais, T. M. Haard, Y. Lee, N. Mulders, and W. P. Halperin, Phys. Rev. Lett. 85, 4325 (2000); G. Gervais, R. Nomura, T. M. Haard, Y. Lee, N. Mulders, and W. P. Halperin, J. Low Temp. Phys. 122, 1 (2001)]. We find reasonable agreement between the theory and the experiment.

Precessing Domain NMR in Normal and Superfluid Fermi Liquids

Coherently precessing two domain spin states, in both normal and superfluid Fermi liquids, can be formed owing to reactive spin currents. A short review of these states is given. Existing and potential applications of coherently precessing domains are discussed.

Equations for the order parameter and effective magnetic field for nonunitary phases of superfluid Fermi liquids with spin-triplet p-wave pairing

On the basis of generalized Fermi-liquid approach we have derived the systems of coupled equations for the components of the order parameter and effective magnetic field for nonunitary phases of neutral paramagnetic superfluid Fermi liquids with spin-triplet pairing in strong static uniform magnetic field at arbitrary temperatures from the interval 0⩽ T⩽ T c ( T c is the normal–superfluid transition temperature). These equations are presented here for dense superfluid neutron matter (existing inside fluid core of neutron stars) with triplet p-wave pairing of 3 He –A 2 type and using the effective Skyrme interaction between neutrons.

Symmetry of Equilibrium State and Hydrodynamics Equation of a Superfluid Fermi-liquid

Symmetry of Equilibrium State and Hydrodynamics Equation of a Superfluid Fermi-liquid

Some questions in the theory of a superfluid Fermi liquid with triplet pairing in a magnetic field

General expressions are obtained in explicit form for the anomalous and normal distribution functions of quasiparticles in nonunitary phases of a superfluid paramagnetic Fermi liquid consisting of electrically neutral fermions with triplet pairing (the pairs have spin s=1 and an arbitrary odd value of the orbital angular momentum l) in a uniform static magnetic field. A generalized Fermi-liquid approach is used which takes into account the exchange Fermi-liquid interaction but does not specify the form of the energy functional of the superfluid Fermi liquid. The results are valid at any temperature in the interval 0⩽T⩽Tc, where Tc is the temperature of the phase transition from the normal to the superfluid state. When an explicit form of the energy functional is specified, the general formulas for the distribution function can be used to describe the various nonunitary phases of a superfluid Fermi liquid of the He3 type in a high magnetic field. In particular, for He3-A1, He3-A2, and the nonunitary two-dimensional phase of He3 in a high magnetic field at 0⩽T⩽Tc, an energy functional quadratic in the distribution function is used to find a system of coupled equations for the order parameter and the effective magnetic field and to obtain an expression is obtained for the nonlinear magnetic susceptibility.

Quasiparticles and phase fluctuations in high Tc superconductors

We argue based on theoretical considerations and analysis of experimental data that quasiparticle excitations near the nodes determine the low temperature properties in the superconducting state of cuprates. Quantum effects of phase fluctuations are shown to be quantitatively important, but thermal effects are small for T ⪡ T c . An anisotropic superfluid Fermi liquid phenomenology is presented for the effect of quasiparticle interactions on the temperature and doping dependence of the low T penetration depth.