The relaxation time of a chiral quantum R-L circuit

TL;DR

This study investigates the GHz admittance of a chiral quantum R-L circuit in the quantum Hall regime, revealing resistance-independent relaxation time governed by electron transit time, with conductance steps observed in admittance components.

Contribution

It introduces a scattering theory explaining the resistance-independent relaxation time in a chiral quantum R-L circuit, supported by experimental admittance measurements.

Findings

Admittance exhibits conductance steps in both real and imaginary parts.

The phase of admittance remains transmission-independent.

Relaxation time equals the electronic transit time in the circuit.

Abstract

We report on the GHz complex admittance of a chiral one dimensional ballistic conductor formed by edge states in the quantum Hall regime. The circuit consists of a wide Hall bar (the inductor L) in series with a tunable resistor (R) formed by a quantum point contact. Electron interactions between edges are screened by a pair of side gates. Conductance steps are observed on both real and imaginary parts of the admittance. Remarkably, the phase of the admittance is transmission-independent. This shows that the relaxation time of a chiral R-L circuit is resistance independent. A current and charge conserving scattering theory is presented that accounts for this observation with a relaxation time given by the electronic transit time in the c cuit.