Dynamically Characterizing the Structures of Dirac Points via Wave Packets

TL;DR

This paper explores how wave packet dynamics can reveal topological features of Dirac points in modified graphene models, including their emergence, annihilation, and associated topological invariants.

Contribution

It introduces a method to characterize topological band structures and Dirac points using wave packet behavior, including the detection of winding numbers and hybrid points.

Findings

Emergence of additional Dirac points with third-nearest-neighbor coupling.

Wave packet motion exhibits Zitterbewegung at hybrid points.

Winding numbers can be inferred from wave packet center-of-mass and spin textures.

Abstract

Topological non-trivial band structures are the core problem in the field of topological materials. In this paper, we investigate the topological band structure in a system with controllable Dirac points from the perspective of wave packet dynamics. By adding a third-nearest-neighboring coupling to the graphene model, additional pairs of Dirac points emerge. The emergence and annihilation of Dirac points result in hybrid and parabolic points, and we show that these band structures can be revealed by the dynamical behaviors of wave packets. Particularly, for the gapped hybrid point, the motion of the wave packet shows a one-dimensional \emph{Zitterbewegung} motion. Furthermore, we also show that the winding number associated with the Dirac point and parabolic point can be determined via the center-of-mass and spin texture of wave packets, respectively. The results of this work could motivate new experimental methods to characterize the system's topological signatures through wave packet dynamics, which may also find application in systems of other exotic topological materials.