Chirality of Zitterbewegung and its relation to Berry curvature in Dirac systems

TL;DR

This paper uncovers a precise analytical link between Zitterbewegung motion and Berry curvature in 2D Dirac systems, connecting quantum dynamics with topological band properties.

Contribution

It establishes a state-independent relation between Zitterbewegung and Berry curvature, revealing a direct connection between quantum dynamics and topological band geometry.

Findings

A time-independent antisymmetric observable called areal rate of Zitterbewegung is directly determined by Berry curvature.

The sign of this observable indicates the rotation sense and relates to Dirac points' contributions to the Chern number.

The relation holds for generic two-band Dirac models and is independent of initial states.

Abstract

We establish an exact analytical relation between Zitterbewegung dynamics and the band geometry in two-dimensional Dirac systems. By identifying a time-independent antisymmetric observable-the \textit{areal rate of Zitterbewegung}-we show that this quantity is directly determined by the Berry curvature. Its sign defines the sense of rotation and reproduces the contributions of Dirac points to the Chern number. This relation is independent of the initial state and holds for generic two-band Dirac models. Our findings reveal a direct connection between interband quantum dynamics and topological band geometry beyond the semiclassical regime.