2024/12/31 by Chen, Xi, Wang, Fa-Jie, Bi, Zhen +1 · 1 citation
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Mesoscale and Nanoscale Physics (cond-mat.mes-hall)
paper · doi:10.48550/arxiv.2501.00572
Ensembles that respect symmetries on average exhibit richer topological states than those in pure states with exact symmetries, leading to the concept of average symmetry-protected topological states (ASPTs). The free-fermion counterpart of ASPT is the so-called statistical topological insulator (STI) in disordered ensembles. In this work, we demonstrate the existence of an intrinsic STI, which has no clean counterpart. Using a real space construction (topological crystal), we find an axion STI characterized by the average axion angle θ=π, protected by an average C4T symmetry with (C4T)4=1. While the exact C4T symmetry reverses the sign of θ angle, and hence seems to protect a ℤ2 classification of θ = 0,π, we prove that the θ = π state cannot be realized in the clean limit if (C4T)4 = 1. Therefore, the axion STI lacks band insulator correspondence and is thus intrinsic. To illustrate this state, we construct a lattice model and numerically explore its phase diagram, identifying an axion STI phase separated from both band insulators and trivial Anderson insulators by a metallic phase, revealing the intrinsic nature of the STI. We also argue that the intrinsic STI is robust against electron-electron interactions. Our work thus provides the first intrinsic crystalline ASPT and its lattice realization.