Nonequilibrium Relaxation and Odd-Even Effect in Finite-Temperature Electron Gases

TL;DR

This paper develops a method to analyze the full spectrum of relaxation modes in two-dimensional Fermi liquids, revealing the persistence of long-lived odd-parity modes up to relatively high temperatures and their dependence on interaction strength.

Contribution

It introduces an efficient approach to evaluate the entire relaxation spectrum of Fermi liquids, extending understanding beyond low temperatures and classifying odd-parity modes in detail.

Findings

Odd-parity modes remain long-lived up to 0.15T_F.

Few long-lived odd-parity modes dominate the spectrum.

The ratio of odd- to even-parity lifetimes is tunable via Coulomb interaction.

Abstract

Pauli blocking in Fermi liquids imposes strong phase-space constraints on quasiparticle lifetimes, leading to a well-known quadratic-in-temperature decay rate of quasiparticle modes at low temperatures. In two-dimensional systems, however, even longer-lived modes are predicted (dubbed ``odd-parity'' modes) that involve a collective deformation of the Fermi distribution. Here, we present an efficient method to evaluate the full spectrum of relaxational eigenmodes of a Fermi liquid within kinetic theory. We employ this method to study the experimentally relevant case of a Fermi liquid with screened Coulomb interactions and map out the decay rates of quasiparticle modes beyond the asymptotic low-temperature limit up to the Fermi temperature, thus covering the entire temperature range of typical experiments. We confirm the existence of anomalously long-lived odd-parity modes and provide a comprehensive classification and detailed analysis of the relaxation spectrum. In particular, we find that (i) the odd-parity effect in the decay rates extends to temperatures as large as $T=0.15T_F$, (ii) there is only a small number of long-lived odd-parity modes, with an infinite number of remaining modes that show standard Fermi-liquid scaling, and (iii) the ratio between the odd- and even-parity lifetimes is tunable with the Coulomb interaction strength, in addition to temperature, which reflects a difference in the microscopic relaxation mechanism of the modes. Our findings provide a comprehensive description of the nonequilibrium relaxation behavior of two-dimensional electron gases and bridge a significant gap in our understanding of these systems.