Asymmetry-driven plasmon instabilities in confined hydrodynamic electron flows

TL;DR

This paper establishes a direct relation between structural asymmetry and plasmon instability in confined 2D electron systems, revealing that asymmetry promotes instability and providing a theoretical framework for predicting the threshold current for plasmon generation.

Contribution

It develops a perturbation theory linking asymmetry to plasmon instability and derives a lower bound on the instability threshold current in asymmetric 2D electron flows.

Findings

Asymmetry increases plasmon gain until viscous dissipation dominates.

Instability occurs at arbitrarily weak drive currents in asymmetric structures.

A lower bound on the threshold current is derived, with a Reynolds number of 2√3.

Abstract

Direct current in confined two-dimensional (2d) electron systems can become unstable with respect to the excitation of plasmons. Numerous experiments and simulations hint that structural asymmetry somehow promotes plasmon generation, but a constitutive relation between asymmetry and instability has been missing. We provide such relation in the present paper and show that bounded perfect 2d electron fluids in asymmetric structures are unstable under arbitrarily weak drive currents. To this end, we develop a perturbation theory for hydrodynamic plasmons and evaluate corrections to their eigenfrequency induced by carrier drift, scattering, and viscosity. We show that plasmon gain continuously increases with degree of plasmon mode asymmetry until it surrenders to viscous dissipation that also benefits from asymmetry. The developed formalism allows us to put a lower bound on the instability threshold current, which corresponds to the Reynolds number $R_{\min} = 2\sqrt{3}$ for one-dimensional plasmons in 2d channel under constant voltage bias.