Symmetries in the collective excitations of an electron gas in core-shell nanowires

We study the collective excitations and inelastic light-scattering cross section of an electron gas confined in a GaAs/AlGaAs coaxial quantum well. These systems can be engineered in a core-multishell nanowire and inherit the hexagonal symmetry of the underlying nanowire substrate. As a result, the electron gas forms both quasi-one-dimensional channels and quasi-two-dimensional channels at the quantum-well bents and facets, respectively. Calculations are performed within the random-phase approximation and time-dependent density functional theory approaches. We derive symmetry arguments which allow one to enumerate and classify charge and spin excitations and determine whether excitations may survive to Landau damping. We also derive inelastic light-scattering selection rules for different scattering geometries. Computational issues stemming from the need to use a symmetry-compliant grid are also investigated systematically