### abstract

- By taking advantage of the GaAs (631) corrugation self-assembled on top of multi-quantum well heterostructure interfaces, the modulation of the confined state wave functions (eigenstates) has been achieved, attaining quasi-one-dimensional or fractional dimension eigenstates. Two different theoretical approaches were used to compute the energy shift of subband optical transitions as a function of the interface corrugation geometrical configuration. For large nominal quantum well widths and small corrugation amplitude, the perturbation theory was employed, while a modified Lanczos algorithm assisted us to calculate the shifts when the corrugation amplitude was comparable to the nominal quantum well width. Experimentally, the heterostructures were grown by molecular beam epitaxy on (001) and (631) oriented substrates, where the quasi-one-dimensional ordering was reached by changing the As to Ga molecular beam fluxes ratio. It was found that the corrugated interfaces (i) break the wave function%27s in-plane symmetry, allowing transitions that, in principle, must be forbidden and (ii) induce blue shifts or red shifts in the order of 10 meV to the energy spectrum of the quantum wires depending on the lateral and vertical periodicities, exhibiting the presence of a lateral confinement system. The main result is the effective modulation of eigenstates through the interface corrugation control. Additionally, it was found that the interface modulation effect is greater for harmonic (n > 1) heavy (and light) hole subbands than for the ground states. © 2020 Author(s).
- By taking advantage of the GaAs (631) corrugation self-assembled on top of multi-quantum well heterostructure interfaces, the modulation of the confined state wave functions (eigenstates) has been achieved, attaining quasi-one-dimensional or fractional dimension eigenstates. Two different theoretical approaches were used to compute the energy shift of subband optical transitions as a function of the interface corrugation geometrical configuration. For large nominal quantum well widths and small corrugation amplitude, the perturbation theory was employed, while a modified Lanczos algorithm assisted us to calculate the shifts when the corrugation amplitude was comparable to the nominal quantum well width. Experimentally, the heterostructures were grown by molecular beam epitaxy on (001) and (631) oriented substrates, where the quasi-one-dimensional ordering was reached by changing the As to Ga molecular beam fluxes ratio. It was found that the corrugated interfaces (i) break the wave function's in-plane symmetry, allowing transitions that, in principle, must be forbidden and (ii) induce blue shifts or red shifts in the order of 10 meV to the energy spectrum of the quantum wires depending on the lateral and vertical periodicities, exhibiting the presence of a lateral confinement system. The main result is the effective modulation of eigenstates through the interface corrugation control. Additionally, it was found that the interface modulation effect is greater for harmonic (n > 1) heavy (and light) hole subbands than for the ground states. © 2020 Author(s).