Relation between Zitterbewegung and the charge conductivity, Berry curvature and the Chern number of multi band systems

TL;DR

This paper links Zitterbewegung, a quantum phenomenon, to charge conductivity, Berry curvature, and Chern number in multi-band systems, highlighting its experimental relevance and providing analytical calculation methods.

Contribution

It establishes a direct relation between Zitterbewegung amplitudes and key topological and transport properties in multi-band electronic systems, offering new analytical tools.

Findings

Charge conductivity expressed via Zitterbewegung amplitudes

Berry curvature and Chern number related to diagonal Zitterbewegung elements

Approach demonstrated with several analytical examples

Abstract

We show that the charge conductivity for impurity free multi band electronic systems can be expressed in terms of the diagonal and non-diagonal elements of the Zitterbewegung amplitudes while the Berry curvature and the Chern number is related only to the diagonal elements. Thus, the phenomenon of the Zitterbewegung can no longer be viewed just as an interesting consequence of quantum physics but it has also an experimental relevance. Moreover, through several examples we demonstrate how efficient our approach is in the analytical calculation of the charge conductivity.