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  • Letter
  • Open Access

Topological edge states of massless fermions with nonquantized and zero Berry phases

F. R. Pratama1,2,* and Takeshi Nakanishi1,†

  • *Contact author: pratama.fr@aist.go.jp
  • †Contact author: t.nakanishi@aist.go.jp
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Phys. Rev. B 110, L161409 – Published 22 October, 2024

DOI: https://doi.org/10.1103/PhysRevB.110.L161409

Abstract

We investigate the bulk-boundary correspondence for massless Dirac fermions in α−T3 lattice where the Berry phase can be continuously tuned from π (graphene) to 0 (T3 or dice lattice) without modifying the energy dispersion. The topological origin of edge states is revealed by the unitary transformation of the Hamiltonian, which maps an α−T3 zigzag ribbon (ZR) onto a stub Su-Schrieffer-Heeger (SSH) chain. In the Majorana representation of the eigenstates, the topological invariant is manifested by the azimuthal winding number on the Bloch sphere. Particularly, T3 ZR exemplifies a topologically nontrivial system with zero Berry phase. Contrary to conventional topological insulators, the gap closing in the corresponding stub SSH chain is not accompanied by a topological phase transition.

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Outline

Information

Phys. Rev. B 110, L161409– Published 22 October, 2024
  • Received 14 June 2024
  • Revised 22 August 2024
  • Accepted 19 September 2024
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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.

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