Fingerprint of Different Spin-Orbit Terms for Spin Transport in HgTe Quantum Wells

TL;DR

This paper derives an effective model for HgTe quantum wells showing how inversion breaking and confining potentials influence spin-orbit interactions, affecting spin transport and the spin-Hall conductance.

Contribution

It introduces a detailed four-band model incorporating spin-orbit effects from inversion breaking and confinement potentials in HgTe quantum wells.

Findings

Inversion breaking potential generates off-diagonal spin terms.

Rashba spin-orbit interaction dominates spin-Hall conductance in asymmetric wells.

Effective Hamiltonian reveals competing spin-orbit terms affecting spin transport.

Abstract

Using $\vec{k}$$\cdot$$\vec{p}$ theory, we derive an effective four band model describing the physics of the typical two-dimensional topological insulator (HgTe/CdTe quantum well) in the presence of out-of-plane in z-direction inversion breaking and in-plane confining potentials. We find that up to third order in perturbation theory, only the inversion breaking potential generates new elements to the four band Hamiltonian that are off-diagonal in spin space. When this new effective Hamiltonian is folded into an effective two band model for the conduction (electron) or valence (heavy hole) bands, two competing terms appear: (1) a Rashba spin-orbit interaction originating from inversion breaking potential in z-direction and (2) an in-plane Pauli term as a consequence of the in-plane confining potential. Spin transport in the conduction band is further analysed within the Landauer-B\"uttiker formalism. We find that for asymmetrically doped HgTe quantum wells, the behaviour of the spin-Hall conductance is dominated by the Rashba term.