Transverse force generated by an electric field and transverse charge imbalance in spin-orbit coupled systems

TL;DR

This paper investigates the transverse force and charge imbalance in spin-orbit coupled systems under an electric field, revealing a non-vanishing transverse force related to energy dispersion and its implications for charge Hall effects.

Contribution

It demonstrates that the transverse force in spin-orbit systems depends on energy dispersion derivatives and persists in Rashba-Dresselhaus systems, with disorder effects leading to cancellation of this force.

Findings

Transverse force can exist without spin current.

The transverse force is related to the second derivative of energy dispersion.

Disorder cancels the transverse force in Rashba-Dresselhaus systems.

Abstract

We use linear response theory to study the transverse force generated by an external electric field and hence possible charge Hall effect in spin-orbit coupled systems. In addition to the Lorentz force that is parallel to the electric field, we find that the transverse force perpendicular to the applied electric field may not vanish in a system with an anisotropic energy dispersion. Surprisingly, in contrast to the previous results, the transverse force generated by the electric field does not depend on the spin current, but in general, it is related to the second derivative of energy dispersion only. Furthermore, we find that the transverse force does not vanish in the Rashba-Dresselhaus system. Therefore, the non-vanishing transverse force acts as a driving force and results in charge imbalance at the edges of the sample. The estimated ratio of the Hall voltage to the longitudinal voltage is $\sim 10^{-3}$. The disorder effect is also considered in the study of the Rashba-Dresselhaus system. We find that the transverse force vanishes in the presence of impurities in this system because the vertex correction and the anomalous velocity of the electron accidently cancel each other.