Chirality of Zitterbewegung and its relation to Berry curvature in Dirac systems
TLDR
This paper reveals an exact analytical relation between Zitterbewegung dynamics and Berry curvature in 2D Dirac systems, linking quantum dynamics to topological band geometry.
Key contributions
- Establishes an exact analytical relation between Zitterbewegung dynamics and band geometry in 2D Dirac systems.
- Identifies a time-independent 'areal rate of Zitterbewegung' directly determined by Berry curvature.
- Shows its sign defines rotation sense and reproduces Dirac point contributions to the Chern number.
- Connects interband quantum dynamics to topological band geometry beyond the semiclassical regime.
Why it matters
This paper provides a fundamental link between quantum dynamics and topological band geometry. It offers a new observable to probe topological properties, extending our understanding beyond semiclassical approximations. This could impact future research in quantum materials.
Original 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.
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