Second-Order Topological Phases in Non-Hermitian Systems

Tao Liu, Yu-Ran Zhang, Qing Ai, Zongping Gong, Kohei Kawabata, Masahito Ueda, and Franco Nori
Phys. Rev. Lett. 122, 076801 – Published 20 February 2019
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Abstract

A d-dimensional second-order topological insulator (SOTI) can host topologically protected (d2)-dimensional gapless boundary modes. Here, we show that a 2D non-Hermitian SOTI can host zero-energy modes at its corners. In contrast to the Hermitian case, these zero-energy modes can be localized only at one corner. A 3D non-Hermitian SOTI is shown to support second-order boundary modes, which are localized not along hinges but anomalously at a corner. The usual bulk-corner (hinge) correspondence in the second-order 2D (3D) non-Hermitian system breaks down. The winding number (Chern number) based on complex wave vectors is used to characterize the second-order topological phases in 2D (3D). A possible experimental situation with ultracold atoms is also discussed. Our work lays the cornerstone for exploring higher-order topological phenomena in non-Hermitian systems.

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  • Received 9 October 2018

DOI:https://doi.org/10.1103/PhysRevLett.122.076801

© 2019 American Physical Society

Physics Subject Headings (PhySH)

  1. Physical Systems
Condensed Matter, Materials & Applied PhysicsAtomic, Molecular & Optical

Authors & Affiliations

Tao Liu1,*, Yu-Ran Zhang1,2, Qing Ai1,3, Zongping Gong4,†, Kohei Kawabata4,‡, Masahito Ueda4,5,§, and Franco Nori1,6,∥

  • 1Theoretical Quantum Physics Laboratory, RIKEN Cluster for Pioneering Research, Wako-shi, Saitama 351-0198, Japan
  • 2Beijing Computational Science Research Center, Beijing 100193, China
  • 3Department of Physics, Applied Optics Beijing Area Major Laboratory, Beijing Normal University, Beijing 100875, China
  • 4Department of Physics, University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
  • 5RIKEN Center for Emergent Matter Science (CEMS), Wako, Saitama 351-0198, Japan
  • 6Department of Physics, University of Michigan, Ann Arbor, Michigan 48109-1040, USA

  • *tao.liu@riken.jp
  • gong@cat.phys.s.u-tokyo.ac.jp
  • kawabata@cat.phys.s.u-tokyo.ac.jp
  • §ueda@phys.s.u-tokyo.ac.jp
  • fnori@riken.jp

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Issue

Vol. 122, Iss. 7 — 22 February 2019

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