2020/03/31 by Yixing Fu, Justin H. Wilson, J. H. Pixley
Mathematics · Physics and Astronomy · #Brillouin zone #Condensed matter physics #Mathematics #Physics #Quantum #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quasiperiodic function #Symmetry protected topological order #Topological Materials and Phenomena #Topological degeneracy #Topological insulator #Topological order #Topology (electrical circuits) #cond-mat.dis-nn #cond-mat.quant-gas #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.104.l041106
published as Phys. Rev. B 104, 041106 (2021) · 6 pages, 4 figures, and supplement materials. Updated results on the flatness ratio, the Berry curvature, and the Chern number of individual bands
arxiv created 2021/04/12 · openalex publication_date 2021/07/15 · arxiv updated 2021/07/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The effects of downfolding a Brillouin zone can open gaps and quench the kinetic energy by flattening bands. Quasiperiodic systems are extreme examples of this process, which leads to new phases and critical eigenstates. We analytically and numerically investigate these effects in a two-dimensional topological insulator with a quasiperiodic potential and discover a complex phase diagram. We study the nature of the resulting eigenstate quantum phase transitions; a quasiperiodic potential can make a trivial insulator topological and induce topological insulator-to-metal phase transitions through a unique universality class distinct from random systems. This wealth of critical behavior occurs concomitantly with the quenching of the kinetic energy, resulting in flat topological bands that could serve as a platform to realize the fractional quantum Hall effect without a magnetic field.