• Open Access

Spectrum-Wide Quantum Criticality at the Surface of Class AIII Topological Phases: An “Energy Stack” of Integer Quantum Hall Plateau Transitions

Björn Sbierski, Jonas F. Karcher, and Matthew S. Foster
Phys. Rev. X 10, 021025 – Published 1 May 2020

Abstract

In the absence of spin-orbit coupling, the conventional dogma of Anderson localization asserts that all states localize in two dimensions, with a glaring exception: the quantum Hall plateau transition (QHPT). In that case, the localization length diverges and interference-induced quantum-critical spatial fluctuations appear at all length scales. Normally, QHPT states occur only at isolated energies; accessing them therefore requires fine-tuning of the electron density or magnetic field. In this paper we show that QHPT states can be realized throughout an energy continuum, i.e., as an “energy stack” of critical states wherein each state in the stack exhibits QHPT phenomenology. The stacking occurs without fine-tuning at the surface of a class AIII topological phase, where it is protected by U(1) and (anomalous) chiral or time-reversal symmetries. Spectrum-wide criticality is diagnosed by comparing numerics to universal results for the longitudinal Landauer conductance and wave function multifractality at the QHPT. Results are obtained from an effective 2D surface field theory and from a bulk 3D lattice model. We demonstrate that the stacking of quantum-critical QHPT states is a robust phenomenon that occurs for AIII topological phases with both odd and even winding numbers. The latter conclusion may have important implications for the still poorly understood logarithmic conformal field theory believed to describe the QHPT.

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  • Received 17 December 2019
  • Revised 13 March 2020
  • Accepted 2 April 2020

DOI:https://doi.org/10.1103/PhysRevX.10.021025

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

Björn Sbierski1, Jonas F. Karcher2,3, and Matthew S. Foster3,4

  • 1Department of Physics, University of California, Berkeley, California 94720, USA
  • 2Institut für Nanotechnologie, Institut für QuantenMaterialien und Technologien and Institut für Theorie der Kondensierten Materie, Karlsruhe Institute of Technology, 76021 Karlsruhe, Germany
  • 3Department of Physics and Astronomy, Rice University, Houston, Texas 77005, USA
  • 4Rice Center for Quantum Materials, Rice University, Houston, Texas 77005, USA

Popular Summary

The hallmark of topological insulators and superconductors is the appearance of boundary modes: It is mathematically guaranteed that boundaries always conduct, even in the presence of strong disorder. However, these mathematical arguments are mostly of limited practical use and convey very little physical intuition. This lack of understanding is especially severe in the experimentally most relevant case for 2D surface states. Our numerical study sheds light on this mystery in the case of a topological phase with chiral symmetry, a behavior potentially realized in some superconductors.

In our analysis, we find a surprising connection between surface conduction in chirally symmetric topological materials and another well-studied scenario: the quantum Hall effect, a striking quantization of transverse conductivity in the presence of a magnetic field. Specifically, we find that topological surface states have the same charge transport properties and wave function intensity modulations as critical states known from the quantum Hall plateau transition, in which the transverse conductivity changes between two values. However, there are also differences. Whereas the critical quantum Hall states normally occur at isolated energies, here they are “stacked” into a continuum.

Our results might open the door to a refined and physically more intuitive understanding of three out of five bulk topological phases of matter, where quantum critical states long known in the context of various quantum Hall effects apparently control the surface transport properties over a broad range of energies.

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Vol. 10, Iss. 2 — April - June 2020

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