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

TL;DR

This paper investigates scalar excitations in Fermi liquids, revealing conditions for Pomeranchuk instability and proposing that such instabilities can lead to scalar Bose condensation, affecting the liquid's phase behavior.

Contribution

It introduces a detailed analysis of scalar-mode excitations and demonstrates how Pomeranchuk instability can be stabilized through scalar Bose condensation in Fermi liquids.

Findings

Identification of conditions for zero sound spectrum minima at non-zero momentum.

Demonstration that Pomeranchuk instability can be mitigated by scalar Bose condensation.

Proposal of inhomogeneous condensate states depending on scalar Landau parameter momentum dependence.

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 $-1<f_0 <0$ there are only damped excitations, and for $f_0<-1$ the spectrum becomes unstable against a growth of scalar-mode excitations (a Pomeranchuk instability). An effective Lagrangian for the scalar excitation modes is derived after performing a bosonization procedure. We demonstrate that the Pomeranchuk instability may be tamed by the formation of a static Bose condensate of the scalar modes. The condensation may occur in a homogeneous or inhomogeneous state relying on the momentum dependence of the scalar Landau parameter. Then we consider a possibility of the condensation of the zero-sound-like excitations in a state with a non-zero momentum in Fermi liquids moving with overcritical velocities, provided an appropriate momentum dependence of the Landau parameter $f_0(k)>0$.