The response of thin films of Bi$_2$Se$_3$ to a strong perpendicular magnetic field is investigated by performing magnetic bandstructure calculations for a realistic multi-band tight-binding model. Several crucial features of Landau quantization in a
realistic three-dimensional topological insulator are revealed. The $n=0$ Landau level is absent in ultra-thin films, in agreement with experiment. In films with a crossover thickness of five quintuple layers, there is a signature of the $n=0$ level, whose overall trend as a function of magnetic field matches the established low-energy effective-model result. Importantly, we find a field-dependent splitting and a strong spin-polarization of the $n=0$ level which can be measured experimentally at reasonable field strengths. Our calculations show mixing between the surface and bulk Landau levels which causes the character of levels to evolve with magnetic field.
We address the low-energy effective Hamiltonian of electron doped d0 perovskite semiconductors in cubic and tetragonal phases using the k*p method. The Hamiltonian depends on the spin-orbit interaction strength, on the temperature-dependent tetragona
l distortion, and on a set of effective-mass parameters whose number is determined by the symmetry of the crystal. We explain how these parameters can be extracted from angle resolved photo-emission, Raman spectroscopy, and magneto-transport measurements and estimate their values in SrTiO3.
We determine the effective total spin $J$ of local moments formed from acceptor states bound to Mn ions in GaAs by evaluating their magnetic Chern numbers. We find that when individual Mn atoms are close to the sample surface, the total spin changes
from $J = 1$ to $J = 2$, due to quenching of the acceptor orbital moment. For Mn pairs in bulk, the total $J$ depends on the pair orientation in the GaAs lattice and on the separation between the Mn atoms. We point out that Berry curvature variation as a function of local moment orientation can profoundly influence the quantum spin dynamics of these magnetic entities.
