The influence of Fermi liquid Landau-type interactions on the critical behaviour of superconductors and superfluids in the presence of DC magnetic fields and superflows is studied. Paramagnetic and diamagnetic instability phenomena are described in detail for singlet sand triplet p-paired superconducting Fermi liquids. The impact of Landau interactions on both instability effects is found to be significant. Inhomogeneous Larkin-Ovchinnikov superfluid states are also considered in the case of strongly interacting systems. The influence of Landau interactions on critical depairing superflows for s- and p-paired superfluids is determined. Applications of the results obtained to the description of superconductors, superfluid 3 He and 3 He- 4 He mixtures as well as the rare earth ternary compound ErRh 4 B 4 are discussed.
The influence of Fermi liquid Landau-type interactions on the critical behaviour of superconductors and superfluids in the presence of DC magnetic fields and superflows is studied. Paramagnetic and diamagnetic instability phenomena are described in detail for singlet sand triplet p-paired superconducting Fermi liquids. The impact of Landau interactions on both instability effects is found to be significant. Inhomogeneous Larkin-Ovchinnikov superfluid states are also considered in the case of strongly interacting systems. The influence of Landau interactions on critical depairing superflows for s- and p-paired superfluids is determined. Applications of the results obtained to the description of superconductors, superfluid 3 He and 3 He- 4 He mixtures as well as the rare earth ternary compound ErRh 4 B 4 are discussed.
The Fermi-liquid approach generalized to superfluid systems is used to derive general formulas for the normal and abnormal distribution functions (DF) for quasiparticles of a superfluid Fermi liquid (SFL) consisting of electrically neutral fermions with spin-triplet pairing (the spin of a pair s=1, the orbital angular momentum l of the pair being an arbitrary odd number) in a static uniform magnetic field, taking into account the Landau spin-exchange Fermi-liquid interaction at temperatures 0<T<Tc (Tc is the temperature of phase transition from the normal to the superfluid state). In deriving the DF, the explicit form of the energy functional (EF) for SFL is not used. A system of coupled equations is obtained for the order parameter, energy of quasiparticles, and effective magnetic field for the SFL under investigation in the case of an EF quadratic in DF. The obtained DF and the system of equations are applicable for describing both unitary and nonunitary phases of superfluid He3 in a magnetic field, e.g., for determining the magnetization and magnetic susceptibility of these phases.
A Fermi-liquid approach to the theory of superfluidity is developed, based on a generalization of the combinatoric expression for the entropy to the case in which the state of the Fermi liquid is described not only by a normal but also by an anomalous distribution function. The energy of the superfluid Fermi liquid is given in the form of a functional of these distribution functions. In the weak-coupling approximation the Fermi-liquid approach is equivalent to the BCS theory. The interaction between the Fermi liquid and an electromagnetic field is gauge invariant. In addition to the singlet-pairing theory the triplet-pairing theory is also developed. A unified variational principle that gives rise to the theory of superfluidity (superconductivity) is used to obtain the London equations and the Ginzburg–Landau equation. Applications of this theory are made to the derivation of an equation for ideal two-component hydrodynamics.
The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. We formulate the corrections to the Landau-Boltzmann transport equation starting from Keldysh's field theory for non-equilibrium, strongly interacting Fermions. The theory is applicable to quasiparticle transport in conventional and unconventional superconductors, dense nuclear matter and the low temperature phases of liquid 3He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid 3He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.
This thesis studies two modern mean field theories of the t-J model for high Tc superconductors, namely the Slave-Boson Mean Field Theory and the Spinon-Dopon Mixing Mean Field Theory, from the view point of the traditional Fermi Liquid language. This study mainly focuses on whether the two mean field theories are consistent with Fermi Liquid behaviour in the underdoped regime of the superconducting and pseudogap phases of the t-J model. Historically, experimental results indicate that the superconducting phase can be well described by the conventional Fermi liquid-like quasiparticle picture; while the pseudogap phase exhibits non-trivial non-Fermi Liquid properties. This work aims at interpreting the pseudogap phase in a generalized Fermi Liquid framework and explaining why the simple quasiparticle picture works so well in the superconducting phase even in this strongly correlated superconducting system. Within the Gaussian approximation, we formally derived the Landau interaction in Fermi liquid theory, which serves as the key to classify the behaviour of the quasiparticles in different phases. It is found that the Slave-Boson Mean Field Theory describes the superconducting to the pseudogap phase transition as a transition with an interesting Landau parameter F1s changing from 1+F1s~x to 1+F1s=0, reflecting the occurrence of a quasiparticle instability. A new phase is proposed and its experimental consequences are discussed. On the other hand, we also find that the Spinon-Dopon Mixing Mean Field Theory can be understood in a conventional Fermi Liquid framework; even though quasiparticles in the theory carry larger charges. The issue of superfluid density is also clarified.
In this work, we study the linear stability of superfluid phases of matter irrespective of the nature of microscopic degrees of freedom and the strength of interactions between them. Famously, assuming invariance under Galilean boosts and a phonon-roton single-particle dispersion relation, Landau predicted superfluid helium 4 would become unstable for large enough superfluid velocities. Here, we demonstrate that such instabilities generically follow from a change of sign of one of the eigenvalues of the matrix of second derivatives of the free energy. Our only assumption is the existence of static thermodynamic equilibrium, irrespective of any invariance under boosts or microscopic statistics. Turning on dissipation, we show that a linear dynamical instability also develops, leading to exponential growth in time of perturbations around equilibrium. Specializing to Galilean superfluids and assuming the existence of bosonic quasiparticles, our criterion reproduces Landau's critical velocity for Bose-Einstein condensates. Our criterion also reduces to the well-known maximal supercurrent in weakly coupled superconductors described either by Landau-Ginzburg or Bardeen-Cooper-Schrieffer theory. Further, it correctly reproduces the onset of the instability in relativistic, strongly coupled superfluids without quasiparticles at zero as well as finite temperature, which we construct using gauge/gravity duality. As a less trivial application of our criterion, we show that in dirty superfluids the instability manifests itself first in the thermal diffusion mode instead of the superfluid sound mode. Our work provides a simple, comprehensive, and unified description of the large superflow instability of superfluids and superconductors at any temperature independent of the microscopic details of the system and the strength of interactions.
The microscopic theory of a superfluid Fermi liquid at finite temperature is developed for the case of a pure system with S-wave pairing, and applied to the calculation of the static properties. As a function of $\ensuremath{\theta}\ensuremath{\equiv}\frac{T}{{T}_{c}}$ these properties are determined entirely by the Landau parameters F0, F1, Z0, etc., characterizing quasiparticle interactions in the normal phase. In particular the spin susceptibility $\ensuremath{\chi}$ and the density of the normal component ${\ensuremath{\rho}}_{n}$ are given by $\frac{\ensuremath{\chi}(\ensuremath{\theta})}{\ensuremath{\chi}(1)}=(1+\frac{1}{4}{Z}_{0})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{4}{Z}_{0}f(\ensuremath{\theta})]},$ $\frac{{\ensuremath{\rho}}_{n}}{\ensuremath{\rho}}=(1+\frac{1}{3}{F}_{1})\frac{f(\ensuremath{\theta})}{[1+\frac{1}{3}{F}_{1}f(\ensuremath{\theta})]},$ where the universal function $f(\ensuremath{\theta})\ensuremath{\equiv}\ensuremath{-}{[\ensuremath{\nu}(0)]}^{\ensuremath{-}1}{\ensuremath{\Sigma}}_{\mathrm{p}}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is the "effective density of states near the Fermi surface" relative to its value $\ensuremath{\nu}(0)$ in the normal phase. Thus the often-quoted expression ${\ensuremath{\rho}}_{n}=\frac{1}{3}{\ensuremath{\Sigma}}_{\mathrm{p}}{\mathrm{p}}^{2}(\frac{\mathrm{dn}}{d{E}_{\mathrm{p}}})$ is valid for an interacting system only in the limit $T\ensuremath{\rightarrow}0$. In the latter part of the paper a simple phenomenological theory of "Fermi-liquid" effects on $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ is developed for arbitrary conditions (including the presence of impurities and pairing with $l\ensuremath{\ne}0$); it is found that under most circumstances explicit expressions for $\ensuremath{\chi}$ and ${\ensuremath{\rho}}_{n}$ may be obtained which involve only the Landau parameters and a suitably generalized effective density of states. The theory should apply to the possible superfluid phase of He3 and to most superconductors. It is suggested that the Knight shift in nontransition-metal superconductors should display some "Fermi-liquid" effects. The weak-field dc penetration depth $\ensuremath{\lambda}(T)$ is shown to be insensitive to such effects both in the Pippard limit and near Tc; however, in a London superconductor at lower temperatures the correction to $\ensuremath{\lambda}(T)$ should be observable and yield a direct estimate of F1.