  We investigate the electronic band structure of modulation-doped GaAs/AlGaAs
core-shell nanowires for both n- and p-doping. We developed an 8-band
Burt-Foreman k.p Hamiltonian approach to describe coupled conduction and
valence bands in heterostructured nanowires of arbitrary composition, growth
directions, and doping. Coulomb interactions with the electron/hole gas are
taken into account within a mean-field self-consistent approach. We map the
ensuing multi-band envelope function and Poisson equations to optimized,
non-uniform real-space grids by the finite element method. Self-consistent
charge density, single-particle subbands, density of states and absorption
spectra are obtained at different doping regimes. For n-doped samples, the
large restructuring of the electron gas for increasing doping results in the
formation of quasi-1D electron channels at the core-shell interface. Strong
heavy-hole/light-hole coupling of hole states leads to non parabolic
dispersions with mass inversion, similarly to planar structures, which persist
at large dopings, giving rise to direct LH and indirect HH gaps. In p-doped
samples the hole gas forms an almost isotropic, ring-like cloud for a large
range of doping. Here, as a result of the increasing localization, HH and LH
states uncouple, and mass inversion takes place at a threshold density. A
similar evolution is obtained at fixed doping as a function of temperature. We
show that signatures of the evolution of the band structure can be singled out
in the anisotropy of linearly polarized optical absorption.
