Shot noise induced charge and potential fluctuations of edge states in proximity of a gate

TL;DR

This paper investigates how shot noise causes charge and potential fluctuations in edge states near a gate, affecting dephasing rates in mesoscopic conductors, by analyzing RC-time and electrochemical capacitance.

Contribution

It introduces a novel resistance related to shot noise-induced charge fluctuations and explores the effects of multiple edge states and dephasing probes.

Findings

Shot noise induces charge fluctuations characterized by a new resistance.

Electrochemical capacitance depends on the density of states of edge states.

Potential fluctuations influence dephasing rates in mesoscopic systems.

Abstract

We evaluate the RC-time of edge states capacitively coupled to a gate located away from a QPC which allows for partial transmission of an edge channel. At long times or low frequencies the RC-time governs the relaxation of charge and current and governs the fluctuations of the equilibrium electrostatic potential. The RC-time in mesoscopic structures is determined by an electrochemical capacitance which depends on the density of states of the edge states and a charge relaxation resistance. In the non-equilibrium case, in the presence of transport, the shot noise leads to charge fluctuations in proximity of the gate which are again determined by the equilibrium electrochemical capacitance but with a novel resistance. The case of multiple edge states is discussed and the effect of a dephasing voltage probe on these resistances is investigated. The potential fluctuations characterized by these capacitances and resistances are of interest since they determine the dephasing rate in Coulomb coupled mesoscopic conductors.