Quasiparticle self-consistent GW calculations of the band structures and related effective mass parameters are carried out for bulk, monolayer and bilayer MoS2. Including excitonic effects within the Mott-Wannier theory, quantitative agreement is obtained between the A, B excitons, measured by absorption (Phys. Rev. Lett. 105,136805 (2010)), and the calculated exciton gap energies at K. The A-B splitting arises from the valence band splitting which in the monolayer is entirely due to spin-orbit coupling and leads to spin-split states, while in the bilayer it is a combined effect of interlayer and spin-orbit coupling.

Calculations of the X-ray linear dichroism (XLD) spectra of the Ga K-edge in GaN and the Gd L3-edge in Gd doped GaN are presented. We show that these spectra can be modeled using partial densities of states standardly available in density functional band structure programs. We find good agreement with recent experiments for Gd on Ga site, showing that there is no need to invoke Gd on N or other sites to explain the spectra as previously claimed in the literature based on multiple scattering simulations.

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The electronic structure of nitrogen vacancies in gadolinium nitride are studied using the full-potential linearized muffin-tin orbital method in the local spin density approximation with Hubbard U corrections (LSDA+U). The vacancy is found to have two localized defect levels in the gap, one of each spin. The third electron of each vacancy in the neutral state dopes the conduction band. The single positive state is found to be the ground state for Fermi levels located anywhere within the band gap. The vacancy has a net magnetic moment of 1 μ B in the neutral charge state. The presence of the vacancy is found to increase the average exchange interactions between Gd atoms and hence the Curie temperature but only by about a factor 2 compared to GdN without vacancies.

The strain effects on the spin-orbit induced splitting of the valence band maximum and conduction band minimum in monolayer MoS2 and the gap in graphene are calculated using first-principles calculations. The dependence of these splittings on the various symmetry types of strain is described by means of an effective Hamiltonian based on the method of invariants and the parameters in the model are extracted by fitting to the theory. These splittings are related to acoustic phonon deformation potentials, or electron-phonon coupling matrix elements which enter the spin-dependent scattering theory of conduction in these materials.