A simple theoretical method for calculating electronic band structure of wurtzite materials based on the linear combination of orbital model is presented. To abtain better description of the conduction band structures, second-nearest-neighbor s and p state interaction are included. We suggest that the zinc-blende InN has a direct band gap of ~2 eV and an indirect band gap of ~0.7 eV located at L-points. Due to band folding effect, the wurtzite InN thus has a direct band gap of ~0.7 eV located at £F3-point.

In this study, the spin-splitting energy of the lowest conduction bands in bulk zincblende and wurtzite structures of III-V semiconductors had been investigated by the linear combination of atomic orbital (LCAO) method, the atomic bond-orbital model (ABOM), and the two-band k¡Dp (2KP) model. Spin-splitting calculation for zincblende structures: We develop a 16-band atomic bond-orbital model (ABOM) to compute the spin splitting induced by bulk inversion asymmetry in zincblende materials. This model is derived from the linear combination of atomic orbital (LCAO) scheme such that the characteristics of the real atomic orbitals can be preserved to calculate the spin splitting. The Hamiltonian of 16-band center-zone ABOM (CZABOM) is based on a similarity transformation performed on the nearest-neighbor LCAO Hamiltonian with a second-order Taylor expansion over k at the £F point. The spin-splitting energies in bulk zincblende semiconductors, GaAs and InSb, are calculated, and the results agree with the LCAO and first-principles calculations. However, we find that the spin-orbit coupling between bonding and antibonding p-like states, evaluated by the 16CZABOM, dominates the spin splitting of the lowest conduction bands in the zincblende materials. Spin-splitting calculation for wurtzite structures: The spin-splitting energies in biaxially strained bulk wurtzite material AlN are calculated using the linear combination of atomic orbital (LCAO) method, and the equi-spin-splitting distributions in k-space near the minimum-spin-splitting (MSS) surfaces are illustrated. These data are compared with those derived analytically by two-band k¡Dp (2KP) model. It is found that the results from these two methods are in good agreement for small k. However, the ellipsoidal MSS surface under biaxial compressive strain does not exist in the 2KP model, because the data points are far from the £F point. Instead, three basic shapes of the MSS surface occur in the wurtzite Brillouin zone: a hyperboloid of two sheets, a hexagonal cone, and a hyperboloid of one sheet, evaluated from the LCAO method across the range of biaxial strains from compressive to tensile. The shapes of the equi-spin-splitting (ESS) surfaces near these MSS surfaces have also three types: a hyperboloid of one sheet, an approximate, asymmetric hyperboloid surface, and an opposing hyperboloid of one sheet.

The effect of spin-orbit coupling had once been thought to be a minor perturbation to the low energy band structure that could be ignored. Instead, a surge in recent theoretical and experimental efforts have shown spin-orbit interactions to have significant consequences. The main objective of this thesis is to investigate the role of the orbital sector and crystal symmetries in governing the spin texture in materials that have strong spin- orbit interactions. This can be accessed through a combination of spin- and angle-resolved photoemission spectroscopy (ARPES and spin-ARPES), both of which are powerful techniques for probing the one-electron band structure plus interactions, and supported by density functional theory calculations (DFT). We focus first on a globally inversion asymmetric material, the layered semiconductor BiTeI, which hosts a giant spin-splitting of its bulk bands. We show that these spin-split bands develop a previously undiscovered, momentum-space ordering of the atomic orbitals. We demonstrate this orbital texture to be atomic element specific by exploiting resonant enhancements in ARPES. These orbital textures drive a hierarchy of spin textures that are then tied to the constituent atomic layers. This opens routes to controlling the spin-splitting through manipulation of the atomic orbitals. This is contrasted against a material where inversion symmetry is globally upheld but locally broken within each monolayer of a two layer unit cell. Through our ARPES and spin-ARPES measurements of 2H-NbSe2, we discover the first experimental evidence for a strong out-of-plane spin polarisation that persists up to the Fermi surface in this globally inversion sym- metric material. This is found to be intrinsically linked to the orbital character and dimensionality of the underlying bands. So far, previous theories underpinning this (and related) materials' collective phases assume a spin- degenerate Fermi sea. We therefore expect this spin-polarisation to play a role in determining the underlying mechanism for the charge density wave phase and superconductivity. Through these studies, this thesis then develops the importance of global versus local inversion symmetry breaking and uncovers how this is intricately tied to the underlying atomic orbital configuration.