Link between Zitterbewegung and topological phase transitions
Xin Shen, Yan-Qing Zhu, Zhi Li
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.