Link of the Zitterbewegung with the spin conductivity and the spin-textures of multiband systems

TL;DR

This paper explores the connection between Zitterbewegung oscillations and spin-related properties in multiband systems, revealing how spin textures and transition amplitudes can indicate the presence of Zitterbewegung.

Contribution

It establishes a direct link between Zitterbewegung and spin textures in multiband Dirac systems, enabling detection of oscillations through spin texture analysis.

Findings

Zitterbewegung relates to spin Hall and optical spin conductivities.

Spin textures can indicate Zitterbewegung presence or suppression.

The approach applies to Dirac-type Hamiltonian models.

Abstract

The Zitterbewegung phenomenon in multiband electronic systems is known to be subtly related to the charge conductivity, Berry curvature and the Chern number. Here we show that some spin-dependent properties as the optical spin conductivity, and intrinsic spin Hall conductivity are also entangled with the Zitterbewegung amplitudes. We also show that in multiband Dirac-type Hamiltonians, a direct link between the Zitterbewegung and the spin textures and spin transition amplitudes can be established. The later allow us to discern the presence or not of the Zitterbewegung oscillations by simply analyzing the spin or pseudo-spin textures. We provide examples of the applicability of our approach for Hamiltonian models that show the suppression of specific Zitterbewegung oscillations.