Odd relaxation in three-dimensional Fermi liquids

TL;DR

This paper demonstrates that three-dimensional Fermi liquids exhibit a hierarchy of relaxation rates between odd and even parity modes, with odd modes relaxing more slowly, revealing a novel non-hydrodynamic behavior similar to two-dimensional systems.

Contribution

It extends the understanding of parity-based relaxation hierarchies from 2D to 3D Fermi liquids, showing that odd-parity modes relax more slowly even without head-on scattering dominance.

Findings

Odd-parity modes relax up to 40% more slowly than even modes.

The odd-even relaxation rate difference depends on the scattering potential.

Signatures of odd-parity relaxation are observable in transport measurements.

Abstract

Recent theoretical works predict a hierarchy of long-lived, non-hydrodynamic modes in two-dimensional Fermi liquids arising from the feature$-$supposedly unique to two dimensions$-$that relaxation by head-on scattering is not efficient in the presence of Pauli blocking. This leads to a parity-based separation of scattering rates, with odd-parity modes relaxing much more slowly than even-parity ones. In this work, we establish that a similar effect exists in isotropic three-dimensional (3D) Fermi liquids, even though relaxation does not proceed solely by head-on scattering. We show that while the relaxation rates of even and odd modes in 3D share the same leading-order $\sim T^2$ low-temperature scaling typical of Fermi liquids, their magnitudes differ, with odd-parity modes relaxing more slowly than even ones for a broad class of interactions. We find a relative difference between odd-parity and even-parity relaxation rates as large as $40\%$ just by Pauli blocking alone, with a strong additional dependence on the scattering potential, such that the odd-even staggering is further enhanced by interactions that favor large-angle scattering. We identify signatures of these odd-parity relaxation rates in the static transverse conductivity as well as the transverse collective mode structure. Our results establish the unexpected existence of a tomographic like regime in higher-dimensional Fermi liquids and suggest experimental probes via transport measurements.