The Interacting Mesoscopic Capacitor Out of Equilibrium

TL;DR

This paper provides an exact analysis of the nonequilibrium response of a mesoscopic capacitor with electron-electron interactions in the quantum Hall regime, revealing linear response behavior and complex charge pulse emissions under sudden gate voltage changes.

Contribution

It offers an exact solution for the full nonequilibrium response of an interacting mesoscopic capacitor, highlighting nonlinear effects and charge pulse emissions beyond simple circuit models.

Findings

Response to gate voltage is strictly linear in the large transparency limit.

Sudden gate voltage shifts emit multiple charge pulses influenced by relaxation and flight times.

Finite reflection introduces nonlinear corrections to charge and current responses.

Abstract

We consider the full nonequilibrium response of a mesoscopic capacitor in the large transparency limit, exactly solving a model with electron-electron interactions appropriate for a cavity in the quantum Hall regime. For a cavity coupled to the electron reservoir via an ideal point contact, we show that the response to any time-dependent gate voltage $V_{\rm g}(t)$ is strictly linear in $V_{\rm g}$. We analyze the charge and current response to a sudden gate voltage shift, and find that this response is not captured by a simple circuit analogy. In particular, in the limit of strong interactions a sudden change in the gate voltage leads to the emission of a sequence of multiple charge pulses, the width and separation of which are controlled by the charge-relaxation time $\tau_{\rm c} = h C_{\rm g}/e^2$ and the time of flight $\tau_{\rm f}$. We also consider the effect of a finite reflection amplitude in the point contact, which leads to nonlinear-in-gate-voltage corrections to the charge and current response.