Prediction of charge separation in GaAs/AlAs cylindrical nanostructures

It is known that in a sequence of flat, type-I $(\mathrm{GaAs}{)}_m/(\mathrm{AlAs}{)}_n/(\mathrm{GaAs}{)}_p/(\mathrm{AlAs}{)}_q\cdot \cdot \cdot$ multiple quantum wells (MQWs), the wave functions of both the valence-band maximum and the conduction-band minimum are localized on the widest well. Thus, electron-hole charge separation is not possible. On the other hand, for short-period superlattices (type II), the electron and hole are localized on different materials (electron on AlAs and hole on GaAs) and different band-structure valleys (hole at $\Gamma$ and electron at $X)$. Using a plane-wave pseudopotential direct-diagonalization approach, we predict that electron-hole charge separation on different layers of the same material (GaAs) and same valley $\left(\Gamma \right)$ is possible in curved (but not in flat) geometries. This is predicted for a set of concentric, nested cylinders of GaAs and AlAs (Russian Doll). Since the flat multiple-quantum-well structure and the Russian Doll structure with the same layer thicknesses have the same band offset diagram, the difference in behavior is not due to the potential. Rather, it reflects different interband coupling and kinetic energy confinement induced by the curvature, present in the nested-cylinder geometry but absent in the MQW. This identifies a geometric degree of freedom (curvature) that can be used to tailor electronic properties of nanostructures.