Disorder effects in two-dimensional flat-band system with next-nearest-neighbor hopping
Phys. Rev. B 114, 014310 – Published 16 July, 2026
DOI: https://doi.org/10.1103/lm27-ktjh
Abstract
For the two-dimensional Lieb lattice, while intrinsic spin-orbit coupling (SOC) 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. Using the transfer-matrix method on a quasi-one-dimensional stripe with transverse periodic boundaries, we 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 the extended nature of topological bulk states when SOC opens a topological gap. Furthermore, correlated disorders are shown to induce inverse Anderson localization 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.
