2010/11/24 by Hadassah Shulman, Shulman, Hadassah, Emil Prodan +1 · 1 citation
Physics and Astronomy · #Atomic and Subatomic Physics Research #Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum and electron transport phenomena #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.1011.5456
openalex publication_date 2010/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper demonstrates the existence of topological models with gapped edge states but protected extended bulk states against disorder. Such systems will be labeled as trivial by the current classification of topological insulators. Our finding calls for a re-examination of the definition of a topological insulator. The analysis is supported by extensive numerical data for a model of non-interacting electrons in the presence of strong disorder. In the clean limit, the model displays a topological insulating phase with spin-Chern number Cs=2 and gapped edge states. In the presence of disorder, level statistics on energy spectrum reveals regions of extended states displaying levitation and pair annihilation. Therefore, the extended states carry a topological invariant robust against disorder. By driving the Fermi level over the mobility edges, it is shown that this invariant is precisely the spin-Chern number. The protection mechanism for the extended state is explained.