2022/01/18 by Shouvik Sur, Alexander C. Tyner, Sur, Shouvik +3
Physics and Astronomy · #FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Quantum chaos and dynamical systems #Quantum many-body systems #Strongly Correlated Electrons (cond-mat.str-el) #Topological Materials and Phenomena
paper · pdf · doi:10.48550/arxiv.2201.07205
openalex publication_date 2022/01/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Benalcazar-Bernevig-Hughes (BBH) models, defined on D-dimensional simple cubic lattice, are paradigmatic toy models for studying D-th order topology and corner-localized, mid-gap states. Under periodic boundary conditions, the Wilson loops of non-Abelian Berry connection of BBH models along all high-symmetry axes have been argued to exhibit gapped spectra, which predict gapped surface-states under open boundary conditions. In this work, we identify 1D, 2D, and 3D topological invariants for characterizing higher order topological insulators. Further, we demonstrate the existence of cubic-symmetry-protected, gapless spectra of Wilson loops and surface-states along the body diagonal directions of the Brillouin zone of BBH models. We show the gapless surface-states are described by 2D-1-component, massless Dirac fermions. Thus, BBH models can exhibit the signatures of first and D-th order topological insulators, depending on the details of externally imposed boundary conditions.