Multiband model of the valence-band electronic structure in cylindrical GaAs nanowires

We compute the hole states in the GaAs free-standing nanowires, and in the GaAs/(Al,Ga)As core-shell nanowires of type I-s, which are grown along the [100] direction. The hole states are extracted from the 4-band Luttinger-Kohn Hamiltonian, which explicitly takes into account mixing between the light and heavy holes. The axial aproximation is adopted, which allowed classification of states according to the total angular monentum (fz when expressed in units of the Planck constant). The envelope functions are expanded in Bessel functions of the first kind. The dispersion relations of the subbands E(kz) obtained by the devised method do not resemble parabolas, which is otherwise a feature of the dispersion relations of the conduction subbands. Furthermore, the energy levels of holes whose total orbital momentum is fz=1/2 are shown to cross for a free-standing wire. The low energy fz=1/2 states are found to anticross, but these anticrossings turn into crossings when the ratio of the inner and outer radius of the core-shell wire takes a certain value. The influence of the geometric parameters on the dispersion relations is considered for both free standing and core-shell nanowires.