Microscopic theory of the activated behavior of the quantized Hall effect

TL;DR

This paper presents a microscopic, self-consistent Hartree-based theory explaining the thermally activated behavior of the quantum Hall effect, emphasizing the role of incompressible strips and sample width on activation energy.

Contribution

It introduces a microscopic model that accounts for the activation energy variation with sample width and magnetic field, diverging from single-particle localization theories.

Findings

Maximum activation energy occurs at the low field edge of the Hall plateau for narrow samples.

For wider samples, the maximum activation energy shifts to the high field edge.

Activation energy is nearly independent of the density of states properties.

Abstract

The thermally activated behavior of the gate defined narrow Hall bars is studied by analyzing the existence of the incompressible strips within a Hartree-type approximation. We perform self-consistent calculations considering the linear response regime, supported by a local conductivity model. We investigate the variation of the activation energy depending on the width of samples in the range of $2d\sim [1-10] \mu m$. We show that the largest activation energy of high-mobility narrow samples, is at the low field edge of Hall filling factor 2 plateau (exceeding half of the cyclotron energy), whereas for relatively wide samples the higher activation energy is obtained at the high field edge of Hall plateau. In contrast to the single-particle theories based on the localization of electronic states, we found that the activation energy is almost independent of the properties of the density of states.