Multifractal zero mode for disordered graphene

TL;DR

This paper investigates the multifractal properties of zero modes in disordered graphene with off-diagonal disorder, revealing how disorder strength influences the localization and fractal dimension of these states.

Contribution

It provides the first calculation of the fractal dimension of zero modes in disordered graphene with edges, highlighting the transition from extended to localized states as disorder increases.

Findings

Zero mode fractal dimension D_2 decreases from 1 to 0 with increasing disorder.

Zero modes are extended at zero disorder and become localized under strong disorder.

Differences between honeycomb and square bipartite lattices are discussed.

Abstract

Off-diagonal disorder with random hopping between the sublattices of a bipartite lattice is described by a Hamiltonian which has chiral (sub-lattice) symmetry. The energy spectrum is symmetric around E=0 and for odd total number of lattice sites an isolated zero mode always exists, which coincides with the mobility edge of an Anderson transition in two dimensions(2D). In the chiral orthogonal symmetry class BDI we compute the fractal dimension $D_{2}$ of the zero mode for graphene samples with edges. In the absence of disorder $D_{2}=1$, which corresponds to a one-dimensional edge states, while for strong disorder $D_{2}$ decays towards 0 and the zero mode becomes localized. The similarities and differences between zero modes in the honeycomb and the square bipartite lattices are pointed out.