Spin orbit coupling in bulk ZnO and GaN

TL;DR

This paper derives and calculates the spin-orbit coupling effects, including Rashba and Dresselhaus terms, in bulk ZnO and GaN semiconductors using group theory and tight-binding models.

Contribution

It provides analytical expressions and numerical coefficients for spin-orbit coupling in wurtzite and zinc-blende ZnO and GaN, advancing understanding of spin effects in these materials.

Findings

Derived explicit spin-orbit coupling expressions for ZnO and GaN.

Calculated Dresselhaus coefficients using tight-binding models.

Identified differences in spin-orbit effects between wurtzite and zinc-blende structures.

Abstract

Using group theory and Kane-like $\mathbf{k\cdot p}$ model together with the L\"owdining partition method, we derive the expressions of spin-orbit coupling of electrons and holes, including the linear-$k$ Rashba term due to the intrinsic structure inversion asymmetry and the cubic-$k$ Dresselhaus term due to the bulk inversion asymmetry in wurtzite semiconductors. The coefficients of the electron and hole Dresselhaus terms of ZnO and GaN in wurtzite structure and GaN in zinc-blende structure are calculated using the nearest-neighbor $sp^3$ and $sp^3s^\ast$ tight-binding models separately.