The two-dimensional Anderson model of localization with random hopping

TL;DR

This paper studies the localization phenomena in a 2D Anderson model with random hopping, revealing critical states at the band center that become localized with added onsite disorder, using multifractal analysis and transfer-matrix methods.

Contribution

It demonstrates the existence of critical eigenstates in the 2D Anderson model with off-diagonal disorder and analyzes their behavior under additional onsite disorder.

Findings

Critical states exist at the band center in the 2D Anderson model.

Critical states exhibit multifractal properties.

Adding onsite disorder localizes the critical states.

Abstract

We examine the localization properties of the 2D Anderson Hamiltonian with off-diagonal disorder. Investigating the behavior of the participation numbers of eigenstates as well as studying their multifractal properties, we find states in the center of the band which show critical behavior up to the system size $N= 200 \times 200$ considered. This result is confirmed by an independent analysis of the localization lengths in quasi-1D strips with the help of the transfer-matrix method. Adding a very small additional onsite potential disorder, the critical states become localized.