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arXiv:1505.03884

Pomeranchuk instability and Bose condensation of scalar quanta in a Fermi liquid

Evgeni E. Kolomeitsev, Dmitry N. Voskresensky

Published May 14, 2015• 1 citation
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Abstract

We study excitations in a normal Fermi liquid with a local scalar interaction. Spectrum of bosonic scalar-mode excitations is investigated for various values and momentum dependence of the scalar Landau parameter $f_0$ in the particle-hole channel. For $f_0 >0$ the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For $-10$.

DOI
10.48550/arxiv.1505.03884

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We study excitations in a normal Fermi liquid with a local scalar interaction. Spectrum of bosonic scalar-mode excitations is investigated for various values and momentum dependence of the scalar Landau parameter f0f_0f0​ in the particle-hole channel. For f0>0f_0 >0f0​>0 the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For −10-10−10.
Nematicity in quantum Hall systems has been experimentally well established at excited Landau levels. The mechanism of the symmetry breaking, however, is still unknown. Pomeranchuk instability of Fermi liquid parameter F_{ℓ}≤-1 in the angular momentum ℓ=2 channel has been argued to be the relevant mechanism, yet there are no definitive theoretical proofs. Here we calculate, using the variational Monte Carlo technique, Fermi liquid parameters F_{ℓ} of the composite fermion Fermi liquid with a finite layer width. We consider F_{ℓ} in different Landau levels n=0, 1, 2 as a function of layer width parameter η. We find that unlike the lowest Landau level, which shows no sign of Pomeranchuk instability, higher Landau levels show nematic instability below critical values of η. Furthermore, the critical value η_{c} is higher for the n=2 Landau level, which is consistent with observation of nematic order in ambient conditions only in the n=2 Landau levels. The picture emerging from our work is that approaching the true 2D limit brings half-filled higher Landau-level systems to the brink of nematic Pomeranchuk instability.
Abstract Using the Landau kinetic equation to study the non-equilibrium behavior of interacting Fermi systems is one of the crowning achievements of Landau’s Fermi liquid theory. While thorough study of transport modes has been done for standard three-dimensional Fermi liquids, an equally in-depth analysis for two dimensional Fermi liquids is lacking. In applying the Landau kinetic equation (LKE) to a two-dimensional Fermi liquid, we obtain unconventional behavior of the zero sound mode c 0 . As a function of the usual dimensionless parameter s = ω / q v F , we find two peculiar results: first, for | s | > 1 we see the propagation of an undamped mode for weakly interacting systems. This differs from the three dimensional case where an undamped mode only propagates for repulsive interactions and the mode experiences Landau damping for any arbitrary attractive interaction. Second, we find that regardless of interaction strength, a propagating mode is forbidden for | s | < 1. This is profoundly different from the three-dimensional case where a mode can propagate, albeit damped. In addition, we present a revised Pomeranchuk instability condition for a two-dimensional Fermi liquid as well as equations of motion for the fluid that follow directly from the LKE. In two dimensions, we find a constant minimum for all Landau parameters for ℓ ⩾ 1 which differs from the three dimensional case. Finally we discuss the effect of a Coulomb interaction on the system resulting in the plasmon frequency ω p exhibiting a crossover to the zero sound mode.
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The quasiparticle excitations and dynamical stability of an atomic Bose-Einstein condensate coupled to a quantum degenerate Fermi gas of atoms at zero temperature is studied. The Fermi gas is assumed to be either in the normal state or to have undergone a phase transition to a superfluid state by forming Cooper pairs. The quasiparticle excitations of the Bose-Einstein condensate exhibit a dynamical instability due to a resonant exchange of energy and momentum with quasiparticle excitations of the Fermi gas. The stability regime for the bosons depends on whether the Fermi gas is in the normal state or in the superfluid state. We show that the energy gap in the quasiparticle spectrum for the superfluid state stabilizes the low-energy excitations of the condensate. In the stable regime, we calculate the boson quasiparticle spectrum, which is modified by the fluctuations in the density of the Fermi gas.
One considers the superfluid (SF) state of a Bose liquid with a strong repulsion between bosons, in which at T=0, along with a weak single-particle Bose-Einstein condensate (BEC), there exists an intensive pair coherent condensate (PCC), analogous to the Cooper condensate in a Fermi liquid with an attraction between the fermions. Such a PCC emerges in a system of bosons due to an oscillating sign-changing momentum dependence of the Fourier component of the pair interaction potential, which is characteristic of a certain family of repulsion potentials. In such cases, the Fourier component is negative in some domain of nonzero momentum transfer, which corresponds to an effective attraction. The collective effects of renormalization (``screening'') of the initial interaction lead to a suppression of the repulsion and an enhancement of the effective attraction. It is the ratio of the BEC density to the full density of the liquid n0/n≪1n_0/n\ll 1n0​/n≪1 that is used as a small parameter---unlike in the Bogolyubov theory for a quasi-ideal Bose gas, in which the small parameter is the ratio of the number of supracondensate excitations to the number of particles in an intensive BEC, (n−n0)/n0≪1(n-n_0)/n_0\ll 1(n−n0​)/n0​≪1. A closed system of nonlinear integral equations for the normal and anomalous self-energy parts is obtained, in the framework of a renormalized perturbation theory built on combined hydrodynamic and field variables. In the framework of the hard-spheres model, a spectrum of quasiparticles is obtained, which is in good accordance with the experimental spectrum of elementary excitations in superfluid 4^44He. The question of applicability of the Landau criterion in the absence of quantum vortices is discussed.