Two-dimensional zero-gap electronic states at a magnetic field

TL;DR

This paper calculates the density of zero-gap electronic states in a two-dimensional system under magnetic field, using supersymmetric methods, revealing how potential perturbations affect the density of states at the Dirac point.

Contribution

It introduces a supersymmetric approach to compute the density of states in 2D zero-gap systems under magnetic fields, accounting for potential perturbations.

Findings

Density of states has a delta peak at the Dirac point without perturbation.

Potential perturbations smear the delta peak, altering the electronic properties.

Method applies to systems like graphene with zero-gap spectra.

Abstract

This work was firstly published in 1986 \cite{we}. No real two-dimensional object with the zero-gap quasi-relativistic spectrum was known in that time. Such an object is well known now: this is graphene. That is why we decided to present it again as a e-print in a slightly modified form. A density of the two-dimensional zero-gap electronic states at the quantizing magnetic field in the presence the Gaussian random potential has been calculated. The problem is reduced to zero-dimensional spinor field theory using the holomorphic supersymmetric representation. The calculated density of states in the case of the mass perturbation has a delta function peak in the Dirac point.This peak smears due to the potential perturbation.