Matrix method analysis of quantum Hall effect device connections

TL;DR

This paper introduces a matrix-based analytical method for modeling quantum Hall effect device connections, simplifying the analysis of complex configurations crucial for electrical metrology and quantum resistance standards.

Contribution

It presents a novel approach using indefinite admittance matrices to analyze QHE device connections, improving ease of analysis over traditional equivalent circuit methods.

Findings

Effective analysis of double- and triple-series QHE connections.

Simplified calculation of device configurations maintaining quantum resistance standards.

Enhanced modeling accuracy for complex QHE device networks.

Abstract

The modelling of electrical connections of single, or several, multiterminal quantum Hall effect (QHE) devices is relevant for electrical metrology: it is known, in fact, that certain particular connections allow i) the realization of multiples or fractions of the quantised resistance, or ii) the rejection of stray impedances, so that the configuration maintains the status of quantum standard. Ricketts-Kemeny and Delahaye equivalent circuits are known to be accurate models of the QHE: however, the numerical or analytical solution of electrical networks including these equivalent circuits can be difficult. In this paper, we introduce a method of analysis based on the representation of a QHE device by means of the \emph{indefinite admittance matrix}: external connections are then represented with another matrix, easily written by inspection. Some examples, including the solution of double- and triple-series connections, are shown.