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Fragility of Surface States in Non-Wigner-Dyson Topological Insulators

Alexander Altland1, Piet W. Brouwer2, Johannes Dieplinger3, Matthew S. Foster4,5, Mateo Moreno-Gonzalez1, and Luka Trifunovic6

  • 1Institute for Theoretical Physics, University of Cologne, 50937 Cologne, Germany
  • 2Dahlem Center for Complex Quantum Systems and Physics Department, Freie Universität Berlin, Arnimallee 14, 14195 Berlin, Germany
  • 3Institute for Theoretical Physics, Universität Regensburg, 93040 Regensburg, Germany
  • 4Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
  • 5Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA
  • 6Laboratoire de Physique Théorique, CNRS, Université Paul Sabatier, 31400 Toulouse, France

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Phys. Rev. X 14, 011057 – Published 27 March, 2024

DOI: https://doi.org/10.1103/PhysRevX.14.011057

Abstract

Topological insulators and superconductors support extended surface states protected against the otherwise localizing effects of static disorder. Specifically, in the Wigner-Dyson insulators belonging to the symmetry classes A, AI, and AII, a band of extended surface states is continuously connected to a likewise extended set of bulk states forming a “bridge” between different surfaces via the mechanism of spectral flow. In this work we show that this mechanism is absent in the majority of non-Wigner-Dyson topological superconductors and chiral topological insulators. In these systems, there is precisely one point with granted extended states, the center of the band, E=0. Away from it, states are spatially localized, or can be made so by the addition of spatially local potentials. Considering the three-dimensional insulator in class AIII and winding number ν=1 as a paradigmatic case study, we discuss the physical principles behind this phenomenon, and its methodological and applied consequences. In particular, we show that low-energy Dirac approximations in the description of surface states can be treacherous in that they tend to conceal the localizability phenomenon. We also identify markers defined in terms of Berry curvature as measures for the degree of state localization in lattice models, and back our analytical predictions by extensive numerical simulations. A main conclusion of this work is that the surface phenomenology of non-Wigner-Dyson topological insulators is a lot richer than that of their Wigner-Dyson siblings, extreme limits being spectrumwide quantum critical delocalization of all states versus full localization except at the E=0 critical point. As part of our study we identify possible experimental signatures distinguishing between these different alternatives in transport or tunnel spectroscopy.

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Popular Summary

Topological insulators are materials whose interiors insulate while their surfaces conduct. In the iconic case of the quantum Hall effect, the conducting surface states spanning different surfaces are connected at high energies through the bulk of the material by delocalized “bridging states.” This surface-bulk connection is called spectral flow, and it underpins some of the most unusual properties of topological matter, such as the ability to pump electrons from one surface to the other through the bulk. In this work, we show that spectral flow is not as closely tied to the physics of topological matter as previously believed.

In particular, we demonstrate that most 3D topological phases do not possess spectral flow. We show how the surface states can be completely detached from the bulk and that there need not be delocalized bridging states in the bulk. The detachment can be accomplished by modifying the surface of the material without changing the topological phase.

The most remarkable physical consequences of these findings concern the response of the surface states to disorder, which is inevitable in real materials. We show that disorder can destroy the conducting properties of almost all surface states in most 3D topological classes. By contrast, all surface states are robustly protected from disorder in topological phases that possess spectral flow (such as the quantum Hall effect). At the same time, we show that surface states can conduct at all energies when the disorder satisfies a certain statistical symmetry, in accordance with previous work.

Our results thus showcase a far richer phenomenology of 3D topological phases than was previously understood, which is of particular relevance in the quest to experimentally identify bulk topological superconductors.

Article Text

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Phys. Rev. X 14, 011057– Published 27 March, 2024
  • Received 4 September 2023
  • Revised 31 January 2024
  • Accepted 23 February 2024
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