Link between \emph{Zitterbewegung} and topological phase transition

TL;DR

This paper explores how itterbewegung and local dynamical properties can indicate topological phase transitions in spin- topological insulators, offering a new dynamical measurement approach.

Contribution

It generalizes the effective Hamiltonian for spin- topological insulators and links itterbewegung dynamics to topological invariants, providing a novel dynamical method for topological characterization.

Findings

itterbewegung direction reflects topological properties.

Developed a quantitative formula for topological invariants.

Validated the theory across different topological systems.

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.