Link between \emph{Zitterbewegung} and topological phase transition

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 \emph{Zitterbewegung} and the topology of systems that reflect 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 \emph{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 new measurement method from the dynamical perspective.

arXiv comment6 pages, 1 figure. Comments are welcome

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• Synthetic non-Abelian topological charges in ultracold atomic gases
• Re-assessing special aspects of Dirac fermions in presence of Lorentz-symmetry violation
• Dynamically Characterizing the Structures of Dirac Points via Wave Packets
• Dynamical properties of quasiparticles in a tunable Kekulé graphene superlattice
• Dynamical Signatures of Floquet Topology in Wave Packet Dynamics
• Link of the Zitterbewegung with the spin conductivity and the spin-textures of multiband systems