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

We show that the charge conductivity for impurity-free multiband electronic systems can be expressed in terms of the nondiagonal 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.