Density of states of a graphene in the presence of strong point defects

TL;DR

This paper investigates the density of states in graphene with strong point defects, revealing a distribution characterized by Thomas-Porter statistics and exploring its effects on magnetic and transport properties.

Contribution

It introduces a novel analysis of eigenfunctions of the inverse T-matrix, linking their behavior to the Thomas-Porter distribution and deriving this from a replica field theory approach.

Findings

Eigenfunctions exhibit random-walk behavior on defect sites.

Density of states follows Thomas-Porter distribution near zero energy.

Distribution influences magnetic and transport properties of graphene.

Abstract

The density of states near zero energy in a graphene due to strong point defects with random positions are computed. Instead of focusing on density of states directly, we analyze eigenfunctions of inverse T-matrix in the unitary limit. Based on numerical simulations, we find that the squared magnitudes of eigenfunctions for the inverse T-matrix show random-walk behavior on defect positions. As a result, squared magnitudes of eigenfunctions have equal {\it a priori} probabilities, which further implies that the density of states is characterized by the well-known Thomas-Porter type distribution. The numerical findings of Thomas-Porter type distribution is further derived in the saddle-point limit of the corresponding replica field theory of inverse T-matrix. Furthermore, the influences of the Thomas-Porter distribution on magnetic and transport properties of a graphene, due to its divergence near zero energy, are also examined.