Application of the Local Chemical Potential to the Quantum Hall Effect in a Ballistic Quantum Wire

Abstract

We have recently made calculations of the Hall resistance of a ballistic two-dimensional electron gas confined in a quantum wire by hard walls (Chu and Butcher 1993 a and b). The calculations are made in the linear transport regime at low temperatures and are based on a formula for the local chemical potential given by Imry (1989). Other authors have sometimes used a different formula which gives different results (Peeters 1988, Akera and Ando 1989 and 1990). Here we outline our calculations and present some of our results. We also give a new definition of the local chemical potential which can be evaluated exactly in the linear transport regime at low temperatures. The outcome is identical to Imry’s formula. An introduction to the theory of electron transport in low-dimensional semiconductor structures is given by Butcher (1993).