Derivation of an electronic equivalent of QHE devices

Models of quantum Hall effect (QHE) devices described by an equivalent circuit are used both to analyze measurement systems and to study QHE physics. Although the most widely used equivalent is the one proposed by Ricketts and Kemeny, various other circuits have been published to suit to different needs in QHE analysis, including a network with only resistors and unity-gain amplifiers. In the following we discuss a general approach to the analysis of the electrical behavior of QHE devices, and show that they can be classified as gyrators. Gyrators are nonreciprocal network elements whose properties are well known from the theory of electrical network. They can be regarded as generalized equivalents of Hall effect devices, thus setting a general framework for the study of the electrical behavior of QHE and the derivation of equivalent circuits. Through the application of this technique, an electronic circuit capable of simulating a QHE device with nonnull longitudinal resistance is derived.