Testing universality of the quantum Hall effect by means of the Wheatstone bridge

Abstract

We report on a study concerning an on-chip quantum Hall effect (QHE) circuit made of two series arrays of two Hall bars set parallel to each other. This array, the design of which is based on the quadruple connection technique, can be studied either as an RK∕i resistance standard (RK is the von Klitzing constant, i is the Hall plateau index) or as a Wheatstone bridge. Metrological characterizations were carried out by varying the temperature, the magnetic field and the bias current. In particular, by measuring the unbalance current with a cryogenic current comparator, it has been possible to compare the four quantum resistances constituting the Wheatstone bridge with a relative uncertainty, never achieved so far, of 8 parts in 1011. This work shows not only the efficiency of the multiple connection technique but also the interest of a QHE Wheatstone bridge made of Hall bars of different natures to realize QHE universality tests with attainable accuracies as low as some parts in 1012. The verification of the QHE universality property with a relative uncertainty one order of magnitude lower than that of the previous universality tests should support, as recommended by the Comité International des Poids et Mesures, the redefinition of the Système International of units based on the fundamental constants of physics.