The Haldane model under quenched disorder

TL;DR

This paper investigates how quenched disorder affects the topological phases of the Haldane model, revealing disorder-induced topological phases and reentrant transitions, extending beyond perturbative predictions.

Contribution

It provides a comprehensive phase diagram of the disordered Haldane model, showing disorder stabilizes topological phases and characterizes gapless and gapped states beyond analytical approximations.

Findings

Disorder stabilizes topological phases in trivial regions of the phase diagram.

Gapless topological phases are supported under both Anderson and binary disorder.

Reentrant topological phase transition observed in binary disorder case.

Abstract

We study the half-filled Haldane model with Anderson and binary disorder and determine its phase diagram, as a function of the Haldane flux and staggered sub-lattice potential, for increasing disorder strength. We establish that disorder stabilizes topologically nontrivial phases in regions of the phase diagram where the clean limit is topologically trivial. At small disorder strength, our results agree with analytical predictions obtained using a first order self-consistent Born approximation, and extend to the intermediate and large disorder values where this perturbative approach fails. We further characterize the phases according to their gapless or gapped nature by determining the spectral weight at the Fermi level. We find that gapless topological nontrivial phases are supported for both Anderson and binary disorder. In the binary case, we find a reentrant topological phase where, starting from a trivial region, a topological transition occurs for increasing staggered potential $\eta$, followed by a second topological transition to the trivial phase for higher values of $\eta$.