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International Conference on Mathematical Methods in Electromagnetic Theory

Hydrodynamic spectra of magnetics with spontaneously broken spin symmetry and B-phase of Fermi-superfluid

Александр Алимович Рожков, Mikhail Yurievich Kovalevsky

Published Nov 27, 2002• 0 citations
Publisher

Abstract

In the present paper, we consider the theory, describing both spiral magnetics and superfluid Fermi-liquid with a triplet pairing. Previously this method was used in the description of a superfluid Fermi-liquid in the singlet case. This approach is a generalization of the classical theory of Fermi-liquid. This semiphenomenological study combines the advantages of both the microscopic and phenomenological description. The method permits the spectra of collective excitations of the system to be obtained taking into account the Fermi-liquid effects.

DOI
10.1109/mmet.1998.709870

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In the present paper, we consider the theory, describing both spiral magnetics and superfluid Fermi-liquid with a triplet pairing. Previously this method was used in the description of a superfluid Fermi-liquid in the singlet case. This approach is a generalization of the classical theory of Fermi-liquid. This semiphenomenological study combines the advantages of both the microscopic and phenomenological description. The method permits the spectra of collective excitations of the system to be obtained taking into account the Fermi-liquid effects.
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.
This review presents a microscopic construction of the thermodynamics and hydrodynamics of superfluid bosons and fermions with singlet pairing, based on the concept of quasiaverages and the hypothesis of reduced description. Here we do not assume that the Hamiltonian possesses any dynamical symmetry. This has permitted obtaining results pertaining to both Galilean-invariant and relativistic systems. Account is taken of dissipative processes. The kinetic coefficients are presented in terms of the correlation functions of the flux operators. The approach is extended to solutions of quantum liquids. The influence of an external ac field on superfluid systems is studied, and the low-frequency asymptotic behavior of the Green's function is found in the hydrodynamic approximation. The symmetry properties of the equilibrium state are formulated, and the thermodynamics is constructed for superfluid Fermi systems with triplet pairing (the superfluid phases 3 He-B and 3 He-A). For the latter the flux densities of the additive integrals of motion are found in a state of equilibrium and the equations of "ideal" hydrodynamics are derived.
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.
A study is made of one of the possible forms of ordering of Fermi systems—superfluid spiral ordering, wherein not only the phase invariance of the state is broken but so are the translational invariance and the invariance with respect to spin rotations. A general method of studying superfluid spiral ordering is formulated on the basis of the Fermi-liquid approach to the consideration of superfluid states. For a one-component Fermi system we obtain the self-consistency equations for four order parameters and the temperature of the simultaneous phase transition to the superfluid and spiral states. The system of equations is investigated in the case of two nonzero order parameters. The transition temperature and the energy gap in the spectrum of elementary fermionic excitations are obtained as functions of the parameter of the spiral. The region of values of the spiral parameter in which the spiral superfluid ordering can exist is determined. The correlation function of the spins in the presence of spiral ordering is investigated.
The rapid experimental progress of ultra-cold dipolar fermions opens up a whole new opportunity to investigate novel many-body physics of fermions. In this article, we review theoretical studies of the Fermi liquid theory and Cooper pairing instabilities of both electric and magnetic dipolar fermionic systems from the perspective of unconventional symmetries. When the electric dipole moments are aligned by the external electric field, their interactions exhibit the explicit d(r(2)-3z(2)) anisotropy. The Fermi liquid properties, including the single-particle spectra, thermodynamic susceptibilities and collective excitations, are all affected by this anisotropy. The electric dipolar interaction provides a mechanism for the unconventional spin triplet Cooper pairing, which is different from the usual spin-fluctuation mechanism in solids and the superfluid (3)He. Furthermore, the competition between pairing instabilities in the singlet and triplet channels gives rise to a novel time-reversal symmetry breaking superfluid state. Unlike electric dipole moments which are induced by electric fields and unquantized, magnetic dipole moments are intrinsic proportional to the hyperfine-spin operators with a Lande factor. Its effects even manifest in unpolarized systems exhibiting an isotropic but spin-orbit coupled nature. The resultant spin-orbit coupled Fermi liquid theory supports a collective sound mode exhibiting a topologically non-trivial spin distribution over the Fermi surface. It also leads to a novel p-wave spin triplet Cooper pairing state whose spin and orbital angular momentum are entangled to the total angular momentum J = 1 dubbed the J-triplet pairing. This J-triplet pairing phase is different from both the spin-orbit coupled (3)He-B phase with J = 0 and the spin-orbit decoupled (3)He-A phase.