Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping

TL;DR

This paper investigates how disorder affects flat-band localization and topological edge states in a 2D Lieb lattice with complex next-nearest-neighbor hopping, revealing robustness of topological states under disorder.

Contribution

It introduces a transfer matrix approach to study disorder effects on flat bands and topological states, highlighting the persistence of edge states under strong disorder.

Findings

Topological edge states mitigate flat-band localization under weak disorder.

Correlated disorder induces inverse Anderson transition with persistent topological states.

Chern number calculations confirm the robustness of topological phases against disorder.

Abstract

For two-dimensional Lieb lattice, while intrinsic spin-orbit coupling is responsible for opening the gap that exhibits the quantum spin Hall effect, topological phase transitions are driven by a real next-nearest-neighbor (NNN) hopping. In this work, we utilize the transfer matrix method to study the flat-band localization mechanism in the presence of complex NNN hoppings. We demonstrate that the geometric localization in flat bands can be alleviated by topological edge states under weak disorder. Furthermore, correlated disorders are shown to induce inverse Anderson transition with the topological edge states persisting under strong disorder, a robustness confirmed by Chern number calculations, which identifies the root cause of this phenomenon. These findings establish a unified platform for investigating topological phase transitions, flat bands, and disorder effects.