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

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.