Topological surface-state destruction via trivializing proximity effect: Lattice localization despite continuum criticality

Abstract: In a significant conceptual revision to the tenfold classification scheme for topological insulators and superconductors, it was recently demonstrated that most three-dimensional (3D) classes are simultaneously "localizable" in two distinct, but intricately connected ways: (1) There is no obstruction to Wannier localization of all bulk eigenstates, and (2) Almost all surface states can be Anderson localized by arbitrarily weak symmetry-preserving quenched disorder. Here we consider the localizable class CI in 3D, and numerically investigate the stability of surface states. We demonstrate that surface states of a bulk class-CI topological lattice model are fragile in that they can be Anderson localized by the combination of weak quenched randomness and hybridization with an additional trivial 2D band (a trivializing proximity effect, TPE). With the TPE, stronger disorder is more destructive to the surface states of the bulk lattice model. By contrast, without additional bands the surface states remain extended, exhibiting robust spectrum-wide quantum criticality. We also investigate the fragility of surface states in effective 2D class-CI continuum Dirac theories, including the chiral limit of the Bistritzer-MacDonald model for twisted bilayer graphene. Although the continuum models exhibit signs of Anderson localization near gap edges for weak disorder, stronger disorder instead appears to heal the surface, restoring criticality whilst filling in spectral energy gaps. Our results provide further evidence that effective continuum field theories fail to capture key aspects of surface-state physics in localizable topological phases.