The effect of inertia on the Dirac electron, the spin Hall current and the momentum space Berry curvature

TL;DR

This paper investigates how inertia influences the Dirac electron, spin Hall current, and Berry curvature in accelerating systems, revealing the interplay of inertial effects, electromagnetic fields, and spin-orbit interactions.

Contribution

It introduces a non relativistic analysis of spin-dependent forces and Berry curvature in accelerating frames using the Foldy-Wouthuysen transformation, highlighting inertial effects on spin dynamics.

Findings

Inertial electric fields affect spin currents via spin-orbit coupling.

Momentum space Berry curvature plays a key role in spin Hall conductivity.

Derived expressions for spin polarization under time-dependent acceleration.

Abstract

We have studied the spin dependent force and the associated momentum space Berry curvature in an accelerating system. The results are derived by taking into consideration the non relativistic limit of a generally covariant Dirac equation under the presence of electromagnetic field where the methodology of Foldy-Wouthuysen transformation is applied to achieve the non relativistic limit. Spin currents appear due to the combined action of the external electric field, crystal field and the induced inertial electric field via the total effective spin-orbit interaction. In an accelerating frame, the crucial role of momentum space Berry curvature in the spin dynamics has also been addressed from the perspective of spin Hall conductivity. For time dependent acceleration, the expression for the spin polarization has been derived.