Phase diagram of the three-dimensional Anderson model of localization with random hopping

TL;DR

This study investigates the localization behavior in a 3D Anderson model with random hopping, revealing the persistence of extended states despite off-diagonal disorder and mapping the phase diagram of metal-insulator transitions.

Contribution

It demonstrates that off-diagonal disorder alone does not fully localize states and provides critical exponents and phase diagram details for the 3D Anderson model.

Findings

Off-diagonal disorder does not localize all states.

Existence of extended states for any off-diagonal disorder.

Computed critical exponents and mapped the phase diagram.

Abstract

We examine the localization properties of the three-dimensional (3D) Anderson Hamiltonian with off-diagonal disorder using the transfer-matrix method (TMM) and finite-size scaling (FSS). The nearest-neighbor hopping elements are chosen randomly according to $t_{ij} \in [c-1/2, c + 1/2]$. We find that the off-diagonal disorder is not strong enough to localize all states in the spectrum in contradistinction to the usual case of diagonal disorder. Thus for any off-diagonal disorder, there exist extended states and, consequently, the TMM converges very slowly. From the TMM results we compute critical exponents of the metal-insulator transitions (MIT), the mobility edge $E_c$, and study the energy-disorder phase diagram.