Anderson Transition in Disordered Bilayer Graphene

TL;DR

This study uses the Kernel Polynomial method to analyze how disorder affects electronic states in bilayer graphene, revealing a transition from metallic to insulating behavior at a critical disorder level.

Contribution

First application of KPM to bilayer graphene showing disorder-induced Anderson transition without exact diagonalization.

Findings

Bilayer graphene exhibits an Anderson metal-insulator transition.

Localized states are identified through geometrical averaging of LDOS.

Transition occurs at a specific critical disorder strength.

Abstract

Employing the Kernel Polynomial method (KPM), we study the electronic properties of the graphene bilayers in the presence of diagonal disorder, within the tight-binding approximation. The KPM method enables us to calculate local density of states (LDOS) without need to exactly diagonalize the Hamiltonian. We use the geometrical averaging of the LDOS's at different lattice sites as a criterion to distinguish the localized states from extended ones. We find that bilayer graphene undergoes Anderson metal-insulator transition at a critical value of disorder strength.