On the structure of strips exhibiting the integral quantum Hall effect in an inhomogeneous 2D electron system

Abstract

A formalism is developed to generalize the results obtained for “incompressible” strips exhibiting the integral quantum Hall effect in a spatially inhomogeneous 2D electron system to the cases of finite temperatures, significant electron density gradients, etc. Specifically, the concept of the “quality” of a given integer quantum Hall effect strip (channel) is introduced; the quality is proportional to the derivative dn(x)/dx in the central part of the channel [n(x) is the electron density distribution over the channel]. For a well-defined channel, this derivative tends to zero. If a noticeable gradient arises in the n(x) distribution, the channel does not exhibit the quantum Hall effect and ceases to exist. The conditions are determined under which a channel exhibiting the integral quantum Hall effect breaks down. The results of calculations are used to interpret the available experimental data.