Teleportation of Berry curvature on the surface of a Hopf insulator

A. Alexandradinata, Aleksandra Nelson, and Alexey A. Soluyanov
Phys. Rev. B 103, 045107 – Published 8 January 2021
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Abstract

The paradigm of topological insulators asserts that an energy gap separates conduction and valence bands with opposite topological invariants. Here, we propose that equal-energy bands with opposite Chern invariants can be spatially separated, onto opposite facets of a finite crystalline Hopf insulator. On a single facet, the number of Berry-curvature quanta is in one-to-one correspondence with the bulk homotopy invariant of the Hopf insulator; this originates from a bulk-to-boundary flow of Berry curvature which is not a type of Callan-Harvey anomaly inflow. In the continuum perspective, such nontrivial boundary states arise as nonchiral, Schrödinger-type modes on the domain wall of a generalized Weyl equation, describing a pair of opposite-chirality Weyl fermions acting as a dipolar source of Berry curvature. A rotation-invariant lattice regularization of the generalized Weyl equation manifests a generalized Thouless pump, which translates charge by one lattice period over half an adiabatic cycle, but reverses the charge flow over the next half.

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  • Received 8 January 2020
  • Revised 17 August 2020
  • Accepted 17 December 2020

DOI:https://doi.org/10.1103/PhysRevB.103.045107

©2021 American Physical Society

Physics Subject Headings (PhySH)

Condensed Matter, Materials & Applied Physics

Authors & Affiliations

A. Alexandradinata1,*, Aleksandra Nelson2, and Alexey A. Soluyanov2,3,†

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801-2918, USA
  • 2Physik-Institut, Universität Zürich, Winterthurerstrasse 190 CH-8057, Zürich, Switzerland
  • 3Department of Physics, St. Petersburg State University, St. Petersburg 199034, Russia

  • *Corresponding author: aalexan7@illinois.edu
  • Deceased.

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Issue

Vol. 103, Iss. 4 — 15 January 2021

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