Application of Block Diagonal Technique to a Hamiltonian Matrix in Performing Spin-splitting Calculations for GaN Wurtzite Materials

Abstract

The bulk inversion asymmetry (Dresselhaus) terms (i.e., B-2, B-1, and B'(1) terms) of wurtzite materials are determined. The 2 x 2 conduction band, 2 x 2 heavy-hole band, 2 x 2 light-hole band, and 2 x 2 crystal-field split-off hole band matrices of wurtzite semiconductors are developed and decoupled by using a block diagonal technique. Importantly, those 2 x 2 block diagonal matrices incorporate not only the interband coupling effect but also the bulk inversion asymmetry effect. Analytical expressions for the conduction and the valence band spin-splitting parameters and energies of GaN wurtzite materials are formulated by solving the block diagonal matrices. The presence of these terms is shown to include the spin-splitting phenomenon.