The quantum hall resistance in quantum wires

Abstract

The Quantum Hall resistance in a semiconductor quantum wire is studied with special attention to the small magnetic field behavior. There are qualitative and quantitative differences between the Hall resistance of a two-dimensional and a quasi-one-dimensional electron gas: 1) the Hall resistance exhibits a finite number of steps, 2) the step resistance for small-intermediate magnetic fields are only approximately quantized into R H = h/ ne 2, n = 1,2,… and 3) the small magnetic field Hall resistance is altered by a geometrical form factor. For very narrow quantum wires it is found experimentally that the Hall resistance is quenched, i.e. R H = 0 for B < B th . In this paper a model is presented which shows how R H approaches zero in the limit of zero magnetic field. Furthermore I find that the experimental four-terminal configuration allows for the existence of bound states.