Application of block diagonal technique to Hamiltonian matrix in performing spin-splitting calculations for GaAs zincblende bulk and quantum wells

Abstract

The 2×2 conduction band, 4×4 hole band, and 2×2 spin-orbit split-off band matrices of zincblende semiconductors are obtained by using a block diagonal technique. Importantly, the block diagonal matrices incorporate not only the interband coupling effect but also the bulk inversion asymmetry effect. Analytical expressions for the conduction band spin-splitting energies of GaAs zincblende bulk and quantum wells grown on [001]-, [111]-, and [110]-oriented substrates are formulated by solving the block diagonal matrices. The results show that odd-in-k terms exist in both the bulk and the quantum well expressions due to the bulk inversion asymmetry effect. The presence of these terms is shown to induce the spin-splitting phenomenon.

k·p Zincblende Hamiltonian and Optical Matrix with Bulk Inversion Asymmetry

“…where is the conduction band spin-splitting parameter for the bulk semiconductor. 9,[17][18][19][20][21] It has been shown experimentally that ¼ 186 eV # A 3 for GaSb. [20][21][22] Consequently, B 0 has a value of 43.1 eV # A 2 for the zincblende semiconductor quantum wells considered in the current analysis.…”

“…8) In semiconductor physics, the conventional kÁp formalism does not take into account the tetrahedral symmetry within a unit cell. [9][10][11][12][13][14][15][16][17] However, this symmetry property can be accounted for by inserting the Kane B 0 parameter terms (i.e., B 0 k x k y , B 0 k y k z , and B 0 k x k z ) into the conventional sp 3 kÁp Hamiltonian matrix. 8,9,17) Accordingly, the aim of this study is to incorporate bulk (or intracell) inversion asymmetry into the matrix elements of the conventional 8 Â 8 kÁp Hamiltonian and optical matrix.…”

“…Although the effects of inversion asymmetry within the unit cell are not accounted for in the conventional kÁp formalism, these effects are though to play a key role in determining the electronic and optical properties of semiconductors. 8,17)…”

Spin-splitting calculation for zincblende semiconductors using an atomic bond-orbital model

“…Many theoretical methods [3][4][5][6] have been developed to calculate the spin-splitting energies of semiconductor superlattices or quantum wells (QWs). The theoretical methods can be classified into four categories [6]: the envelope-function (k • p) method [7][8][9][10][11][12], the pseudopotential method [13][14][15], the tight binding method (also known as the linear combination of atomic orbitals (LCAO) method) [16][17][18][19], and the bond-orbital method (BOM) [20][21][22][23]. In these methods, the 8-band k•p model [7] is the most widely adopted because of its simplicity.…”

Gate voltage and structure parameter modulated spin splitting in AlGaN/GaN quantum wells

“…Due to rapidly developed semiconductor spintronic devices, manipulation of electron spins in semiconductor heterostructures and quantum wells (QWs) has attracted much attention in recent years 1–4. If both time reversal and spatial inversion symmetries in a system are not broken, the electron states in a crystal are known to be doubly degenerate 5. However, because of the electron spin–orbit interaction, inversion asymmetry in space and time will lift the spin degeneracy of electron state at zero magnetic field 6.…”