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  • Letter

Link between Zitterbewegung and topological phase transitions

Xin Shen1,*, Yan-Qing Zhu2,3,†, and Zhi Li3,4,5,‡

  • 1College of Sciences, China Jiliang University, Hangzhou 310018, China
  • 2Department of Physics and Center of Theoretical and Computational Physics, The University of Hong Kong, Pokfulam Road, Hong Kong, China
  • 3Guangdong-Hong Kong Joint Laboratory of Quantum Matter, Frontier Research Institute for Physics, South China Normal University, Guangzhou 510006, China
  • 4Guangdong Provincial Key Laboratory of Nuclear Science, Institute of Quantum Matter, South China Normal University, Guangzhou 510006, China
  • 5Guangdong Provincial Key Laboratory of Quantum Engineering and Quantum Materials, SPTE, South China Normal University, Guangzhou 510006, China

  • *shenx@cjlu.edu.cn
  • †yqzhuphy@hku.hk
  • ‡lizphys@m.scnu.edu.cn
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Phys. Rev. B 106, L180301 – Published 14 November, 2022

DOI: https://doi.org/10.1103/PhysRevB.106.L180301

Abstract

Topological quantum state described by the global invariant has been extensively studied in theory and experiment. In this Letter, we investigate the relationship between Zitterbewegung and the topology of systems that reflects the properties of the local and whole energy bands, respectively. We generalize the usual two-band effective Hamiltonian to characterize the topological phase transition of the spin-J topological insulator. By studying Zitterbewegung dynamics before and after topological phase transition, we find that the direction of quasiparticles' oscillation can well reflect topological properties. Furthermore, we develop a quantitative calculation formula for the topological invariant in the spin-J Chern insulator and give the selection rule of the corresponding dynamics. Finally, we demonstrate that our theory is valid in different topological systems. The topological invariant can be represented by local dynamical properties of the high-symmetry points in the first Brillouin zone, which provides a measurement method from the dynamical perspective.

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Phys. Rev. B 106, L180301– Published 14 November, 2022
  • Received 7 February 2022
  • Revised 4 September 2022
  • Accepted 31 October 2022
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