Dynamic Conductance in Quantum Hall Systems

TL;DR

This paper analyzes the low-frequency admittance of quantum Hall systems using an edge-channel and scattering approach, revealing how the first and second-order frequency terms relate to phase shifts, charge relaxation, and resistance behaviors.

Contribution

It introduces a detailed theoretical framework for understanding the frequency-dependent conductance and admittance in quantum Hall systems, including symmetry properties and resistance calculations.

Findings

First-order term relates to phase shift and emittance, showing capacitive or inductive behavior.

Second-order term describes charge relaxation effects.

Frequency-dependent longitudinal and Hall resistances are characterized.

Abstract

In the framework of the edge-channel picture and the scattering approach to conduction, we discuss the low frequency admittance of quantized Hall samples up to second order in frequency. The first-order term gives the leading order phase-shift between current and voltage and is associated with the displacement current. It is determined by the emittance which is a capacitance in a capacitive arrangement of edge channels but which is inductive-like if edge channels predominate which transmit charge between different reservoirs. The second-order term is associated with the charge relaxation. We apply our results to a Corbino disc and to two- and four-terminal quantum Hall bars, and we discuss the symmetry properties of the current response. In particular, we calculate the longitudinal resistance and the Hall resistance as a function of frequency.