Arithmetic of the integer quantum Hall effect

TL;DR

This paper analyzes the integer quantum Hall effect by separately considering localized and extended states, revealing a saw-tooth variation in current-carrying electrons with magnetic field and providing a comprehensive understanding of IQHE.

Contribution

It offers a detailed analysis of localized and extended states in IQHE, explaining the variation of current-carrying electrons with magnetic field.

Findings

Current-carrying electrons vary in a saw-tooth pattern with magnetic field.

Separate counting of localized and extended states clarifies IQHE behavior.

Provides a simple, complete understanding of the integer quantum Hall effect.

Abstract

text of abstract (Integer quantum Hall effect (IQHE) has been analysed considering the degeneracies of localized and extended states separately. Occupied localized and extended states are counted and their variation is studied as a function of magnetic field. The number of current carrying electrons is found to have a saw-tooth variation with magnetic field. The analysis attempts to answer certain basic questions besides providing a simple but complete understanding of IQHE.)