Localization behavior of the surface of a CI-topological superconductor due to broken spectral flow
ORAL
Abstract
The surface states of “localizable” topological superconductors can be destroyed (Anderson localized) by weak disorder when a symmetry-preserving surface perturbation is applied that can energetically detach the surface states from the bulk. Detachability is a consequence of the absence of spectral flow for most 3D topological phases [1]. At the same time, surface states of localizable topological phases can escape localization through the unusual mechanism of spectrum-wide quantum criticality (SWQC) [2,3,4]. SWQC occurs in the absence of a detaching perturbation, or in its presence as a random perturbation with zero average value. SWQC produces a wide range of surface states showing the same critical behavior as the quantum Hall plateau transition in class AIII [3]; in this case a detaching perturbation pushes Berry curvature into the surface states “from the sky” (bulk-surface interface), allowing localization. In class CI, SWQC can occur with class-C spin-quantum Hall plateau criticality, as found in [2]. At the same time, the Berry curvature mechanism for surface detachment is forbidden by symmetry in this class. We study a 3D class-CI lattice model in the context of broken spectral flow and investigate detaching perturbations. We also consider the interplay between these and disorder, and will determine whether Anderson localization can destroy SWQC in this case. Localization, if observed, should allow us to confirm or refute the spin-quantum Hall criticality of previously observed SWQC by examining the localization transition.
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Publication: [1] A. Altland, P. W. Brouwer, J. Dieplinger, M. S. Foster, M. Moreno-Gonzalez, and L. Trifunovic, Fragility of Surface States in Non-Wigner-Dyson Topological Insulators, Phys. Rev. X 14, 011057 (2024).<br>[2] S. A. A. Ghorashi, Y. Liao, and M. S. Foster, Critical Percolation without Fine-Tuning on the Surface of a Topological Superconductor, Phys. Rev. Lett. 121, 016802 (2018).<br>[3] B. Sbierski, J. F. Karcher, and M. S. Foster, Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An "Energy Stack" of Integer Quantum Hall Plateau Transitions, Phys. Rev. X 10, 021025 (2020).<br>[4] J. F. Karcher and M. S. Foster, How spectrum-wide quantum criticality protects surface states of topological superconductors from Anderson localization: Quantum Hall plateau transitions (almost) all the way down, Ann. Phys. 435, 168439 (2021).
