Pomeranchuk instability and Bose condensation of scalar quanta in a Fermi liquid
E. E. Kolomeitsev🇸🇰 · D. N. Voskresensky🇷🇺
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 in the particle-hole channel. For the conditions are found when the phase velocity on the spectrum of the zero sound acquires a minimum at a non-zero momentum. For there are only damped excitations, and for 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 .