We apply the diagram-technique formalism beyond the Hartree-Fock approximation to a two-dimensional nearly ideal electron gas in a weak perpendicular magnetic field. The case of an almost completely filled upper Landau level [for its filling factor ${\ensuremath{\nu}}_{0}$ holds $(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\ll}1]$ with a quantum number ${N}_{0}\ensuremath{\gg}1$ is considered. We uncover two regimes of renormalization by electron-electron interactions. In the first regime, where ${N}_{0}^{1/2}(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\ll}1,$ these interactions lead to a splitting of the Landau levels. In the second regime, where ${N}_{0}^{1/2}(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\gg}1,$ apart of the splitting, a renormalization of the bare Zeeman splitting occurs. The intermediate case ${N}_{0}^{1/2}(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\approx}1$ cannot be studied within our approach. The applicability of the Fermi-liquid description is investigated for both regimes.We apply the diagram-technique formalism beyond the Hartree-Fock approximation to a two-dimensional nearly ideal electron gas in a weak perpendicular magnetic field. The case of an almost completely filled upper Landau level [for its filling factor ${\ensuremath{\nu}}_{0}$ holds $(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\ll}1]$ with a quantum number ${N}_{0}\ensuremath{\gg}1$ is considered. We uncover two regimes of renormalization by electron-electron interactions. In the first regime, where ${N}_{0}^{1/2}(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\ll}1,$ these interactions lead to a splitting of the Landau levels. In the second regime, where ${N}_{0}^{1/2}(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\gg}1,$ apart of the splitting, a renormalization of the bare Zeeman splitting occurs. The intermediate case ${N}_{0}^{1/2}(1\ensuremath{-}{\ensuremath{\nu}}_{0})\ensuremath{\approx}1$ cannot be studied within our approach. The applicability of the Fermi-liquid description is investigated for both regimes.

arXiv:cond-mat/9806329Physical review. B, Condensed matterApr 15, 19991 citation

Beyond Landau's theory of Fermi liquids

Hagen M. Kleinert

Physics Letters AJul 1, 19814 citations

Quench dynamics of a superfluid Fermi gas

Geoffrey Warner, A. J. Leggett

With an eye toward the interpretation of so-called ``cosmological'' experiments performed on the low-temperature phases of $^{3}\mathrm{He}$ , in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\ensuremath{\lambda}$. In $^{3}\mathrm{He}$ , the quenches induced by the rapid cooling of the ``hot spots'' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap ${\ensuremath{\Delta}}_{\ensuremath{\infty}}={ϵ}_{C}{({e}^{2∕N(0)\ensuremath{\lambda}}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.With an eye toward the interpretation of so-called ``cosmological'' experiments performed on the low-temperature phases of $^{3}\mathrm{He}$, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\ensuremath{\lambda}$. In $^{3}\mathrm{He}$, the quenches induced by the rapid cooling of the ``hot spots'' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap ${\ensuremath{\Delta}}_{\ensuremath{\infty}}={ϵ}_{C}{({e}^{2∕N(0)\ensuremath{\lambda}}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.

Physical Review BApr 21, 200550 citations

Interactions in a dilute fermi gas

E.L. Hazlett

Aug 17, 20120 citations

Fermi-Liquid Description of a Single-Component Fermi Gas with p -Wave Interactions

Shan–Shan Ding, Shizhong Zhang

We study the Fermi liquid properties of a single component Fermi gas with p-wave interactions. In the weak repulsive limit, we obtain exact perturbative expansions for the ground state energy, the chemical potential, and the effective mass of the Landau quasiparticle up to second order in scattering volume a. We also calculated the corresponding Landau functions and Landau parameters and show that they satisfy the general Fermi liquid identities. Using the Landau transport equation, we show that undamped zero sound only appears in the second order in scattering volume, in contrast to the s-wave case.We study the Fermi liquid properties of a single component Fermi gas with p-wave interactions. In the weak repulsive limit, we obtain exact perturbative expansions for the ground state energy, the chemical potential, and the effective mass of the Landau quasiparticle up to second order in scattering volume a. We also calculated the corresponding Landau functions and Landau parameters and show that they satisfy the general Fermi liquid identities. Using the Landau transport equation, we show that undamped zero sound only appears in the second order in scattering volume, in contrast to the s-wave case.

Physical Review LettersAug 15, 201914 citations

With an eye toward the interpretation of so-called ``cosmological'' experiments performed on the low-temperature phases of

^{3}\mathrm{He}

, in which regions of the superfluid are destroyed by local heating with neutron radiation, we have studied the behavior of a Fermi gas subjected to uniform variations of an attractive BCS interaction parameter $\ensuremath{\lambda}$. In

^{3}\mathrm{He}

, the quenches induced by the rapid cooling of the ``hot spots'' back through the transition may lead to the formation of vortex loops via the Kibble-Zurek mechanism. A consideration of the free energy available in the quenched region for the production of such vortices reveals that the Kibble-Zurek scaling law gives at best a lower bound on the defect spacing. Further, for quenches that fall far outside the Ginzburg-Landau regime, the dynamics on the pair subspace, as initiated by quantum fluctuations, tends irreversibly to a self-driven steady state with a gap ${\ensuremath{\Delta}}_{\ensuremath{\infty}}={ϵ}_{C}{({e}^{2∕N(0)\ensuremath{\lambda}}\ensuremath{-}1)}^{\ensuremath{-}1∕2}$. In weak coupling, this is only half the BCS gap, the extra energy being taken up by the residual collective motion of the pairs.