Lifshitz-like argument for low-lying states in a strong magnetic field

TL;DR

This paper introduces a Lifshitz argument to analyze the low-energy spectrum of electrons in strong magnetic fields with random impurities, identifying impurity clusters as key to low-lying states.

Contribution

It presents a novel Lifshitz-based approach to understanding low-energy states in disordered magnetic systems, focusing on impurity cluster configurations.

Findings

Low-energy states are associated with impurity clusters.

Impurity configurations significantly influence the spectral properties.

The approach provides insight into localization phenomena in magnetic fields.

Abstract

We propose a Lifshitz argument in order to analyse the low energy spectrum of an electron moving in a strong magnetic field and scattered by randomly distributed repulsive zero-range impurities. The typical configurations of disorder which give rise to low energy states are identified as clusters of impurities. This allows for an interpretation of low-lying states localized around these clusters.