Two-dimensional electron gas in uniform magnetic and electric fields

TL;DR

This paper provides a quantum statistical explanation for the integer quantum Hall effect by analyzing the thermodynamic potential of a 2D electron gas in crossed magnetic and electric fields, showing quantized Hall conductance at low temperatures.

Contribution

It introduces a thermodynamic approach to explain the integer quantum Hall effect in a 2D electron gas under crossed fields, emphasizing the quantization of Hall conductance.

Findings

Hall conductance is quantized at integer multiples of e^2/h

Quantization persists over a wide range of strong magnetic fields at low temperatures

Magnetic properties are briefly discussed at high temperatures

Abstract

The thermodynamic potential of an ideal nonrelativistic gas of two-dimensional electrons in crossed uniform magnetic and electric fields is constructed. For low temperatures and very weak electric fields, it is shown that the Hall conductance is always quantized at integral multiples of $e^2/h$ over a large range of strong magnetic fields. This could be viewed as a quantum statistical explanation of the integral quantum Hall effect. Magnetic properties of the system at high temperatures are briefly discussed.