Quantum phase transition of dynamical resistance in a mesoscopic capacitor

TL;DR

This paper theoretically investigates the dynamic response of a mesoscopic capacitor in a quantum Hall system, revealing a noise-driven quantum phase transition in the dynamical resistance, including a Kosterlitz-Thouless transition at certain filling factors.

Contribution

It introduces a theoretical framework for understanding noise-induced quantum phase transitions in the dynamical resistance of mesoscopic capacitors with quantum Hall edge states.

Findings

Charge relaxation is quantized at R_q=h/(2e^2) for nu>1/2.

A Kosterlitz-Thouless transition occurs for nu<1/2, altering the resistance behavior.

Noise can induce a phase transition even at integer quantum Hall filling factor nu=1.

Abstract

We study theoretically dynamic response of a mesoscopic capacitor, which consists of a quantum dot connected to an electron reservoir via a point contact and capacitively coupled to a gate voltage. A quantum Hall edge state with a filling factor nu is realized in a strong magnetic field applied perpendicular to the two-dimensional electron gas. We discuss a noise-driven quantum phase transition of the transport property of the edge state by taking into account an ohmic bath connected to the gate voltage. Without the noise, the charge relaxation for nu>1/2 is universally quantized at R_q=h/(2e^2), while for nu<1/2, the system undergoes the Kosterlitz-Thouless transtion, which drastically changes the nature of the dynamical resistance. The phase transition is facilitated by the noisy gate voltage, and we see that it can occur even for an integer quantum Hall edge at nu=1. When the dissipation by the noise is sufficiently small, the quantized value of R_q is shifted by the bath impedance.