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  • Letter

Topological corner states in graphene by bulk and edge engineering

Junjie Zeng1,2,*, Chen Chen3,*, Yafei Ren4, Zheng Liu1, Wei Ren3,†, and Zhenhua Qiao1,5,‡

  • 1CAS Key Laboratory of Strongly-Coupled Quantum Matter Physics, and Department of Physics, University of Science and Technology of China, Hefei, Anhui 230026, China
  • 2Chongqing Key Laboratory for Strongly Coupled Physics and Institute for Structure and Function, Department of Physics, Chongqing University, Chongqing 401331, China
  • 3International Center for Quantum and Molecular Structures, Materials Genome Institute, Physics Department, and Shanghai Key Laboratory of High Temperature Superconductors, Shanghai University, Shanghai 200444, China
  • 4Department of Materials Science and Engineering, University of Washington, Seattle, Washington 98195, USA
  • 5ICQD, Hefei National Laboratory for Physical Sciences at Microscale, University of Science and Technology of China, Hefei, Anhui 230026, China

  • *These authors contributed equally to this work.
  • †Corresponding author: renwei@shu.edu.cn
  • ‡Corresponding author: qiao@ustc.edu.cn
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Phys. Rev. B 106, L201407 – Published 23 November, 2022

DOI: https://doi.org/10.1103/PhysRevB.106.L201407

Abstract

Two-dimensional higher-order topology is usually studied in (nearly) particle-hole symmetric models, so that an edge gap can be opened within the bulk one. But more often the edge anticrossing deviates even into the bulk, where corner states are difficult to pinpoint. We address this problem in a graphene-based Z2 topological insulator with spin-orbit coupling and in-plane magnetization both originating from substrates through a Slater-Koster multiorbital model. The gapless helical edge modes cross inside the bulk, where the magnetization-induced edge gap is also located. After demonstrating its second-order nontriviality in bulk topology by a series of evidence, we show that a difference in bulk-edge on-site energy can adiabatically tune the position of the crossing/anticrossing of the edge modes to be inside the bulk gap. This can help unambiguously identify two pairs of topological corner states with nonvanishing energy degeneracy for a rhombic flake. We further find that the obtuse-angle pair is more stable than the acute-angle one.

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Phys. Rev. B 106, L201407– Published 23 November, 2022
  • Received 18 February 2022
  • Accepted 31 October 2022
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