Conserved Spin and Orbital Angular Momentum Hall Current in a Two-Dimensional Electron System with Rashba and Dresselhaus Spin-orbit Coupling

TL;DR

This paper theoretically investigates the spin and orbital angular momentum Hall effects in a two-dimensional electron system with Rashba and Dresselhaus spin-orbit coupling, revealing their dependence on system parameters and their relation to Berry curvature.

Contribution

It introduces torque corrections to spin and OAM currents, analyzes their interplay, and shows how the total Hall current can be manipulated via Rashba coupling tuning.

Findings

Spin Hall conductivity remains constant when both bands are occupied.

OAM Hall conductivity depends on the Rashba to Dresselhaus ratio.

Spin and OAM Hall conductivities relate to Berry gauge potential.

Abstract

We study theoretically the spin and orbital angular momentum (OAM) Hall effect in a high mobility two-dimensional electron system with Rashba and Dresselhuas spin-orbit coupling by introducing both the spin and OAM torque corrections, respectively, to the spin and OAM currents. We find that when both bands are occupied, the spin Hall conductivity is still a constant (i.e., independent of the carrier density) which, however, has an opposite sign to the previous value. The spin Hall conductivity in general would not be cancelled by the OAM Hall conductivity. The OAM Hall conductivity is also independent of the carrier density but depends on the strength ratio of the Rashba to Dresselhaus spin-orbit coupling, suggesting that one can manipulate the total Hall current through tuning the Rashba coupling by a gate voltage. We note that in a pure Rashba system, though the spin Hall conductivity is exactly cancelled by the OAM Hall conductivity due to the angular momentum conservation, the spin Hall effect could still manifest itself as nonzero magnetization Hall current and finite magnetization at the sample edges because the magnetic dipole moment associated with the spin of an electron is twice as large as that of the OAM. We also evaluate the electric field-induced OAM and discuss the origin of the OAM Hall current. Finally, we find that the spin and OAM Hall conductivities are closely related to the Berry vector (or gauge) potential.