Dyakonov-Shur instability across the ballistic-to-hydrodynamic crossover

TL;DR

This paper investigates the Dyakonov-Shur instability in a 2D Fermi liquid across different scattering regimes, revealing how electron-electron interactions influence the instability's presence and characteristics.

Contribution

It provides a numerical analysis of the instability across the ballistic-to-hydrodynamic crossover, highlighting the role of boundary conditions and scattering rates.

Findings

Hydrodynamic instability observed with fast electron-electron scattering.

Instability disappears due to viscous dissipation in the hydrodynamic regime.

Re-emergence of instability in the ballistic regime under certain boundary conditions.

Abstract

We numerically solve semiclassical kinetic equations and compute the growth rate of the Dyakonov-Shur instability of a two-dimensional Fermi liquid in a finite length cavity. When electron-electron scattering is fast, we observe the well-understood hydrodynamic instability, and its disappearance due to viscous dissipation. When electron-electron scattering is negligible, we find that the instability re-emerges for certain boundary conditions, but not for others. We discuss the implications of these findings for experiments.