Critical wave functions in disordered graphene

TL;DR

This paper investigates the nature of wave functions in disordered graphene, revealing the existence of critical, non-localized states with power-law decay that are robust across different model parameters and system sizes.

Contribution

It provides evidence for critical wave functions in doped graphene using a scaling analysis of inverse participation ratios, highlighting their robustness and intermediate behavior.

Findings

Presence of non-normalizable, critical wave functions with power-law decay.

Critical states are robust against model variations and system size.

Wave functions exhibit behavior between metallic and insulating states.

Abstract

In order to elucidate the presence of non-localized states in doped graphene, an scaling analysis of the wave function moments known as inverse participation ratios is performed. The model used is a tight- binding hamiltonian considering nearest and next-nearest neighbors with random substitutional impurities. Our findings indicate the presence of non-normalizable wave functions that follow a critical (power-law) decay, which are between a metallic and insulating behavior. The power-law exponent distribution is robust against the inclusion of next-nearest neighbors and on growing the system size.