3D simulation of quantum-wire confining potential for a GaAs/AlGaAs 2DEG heterostructure

The aim of this work is the study of electrostatically confined single and coupled quantum wires realized within a high-mobility two-dimensional electron gas (2DEG) at a GaAs/AlGaAs heterointerface. The one-dimensional channels are formed by the potential created by suitably biased surface electrodes. The shape of the bottom of the conduction band energy at the heterojunction has been obtained by numerically solving the three-dimensional Poisson equation over the whole structure at 20 K. Special attention has been paid to the depletion condition for the 2DEG within the quantum wires. To this purpose, the 1D Schr¨odinger equation is solved along the growth direction consistently with the Poisson solution, to accurately calculate the local electron distribution at the heterojunction. Finally, a single-electron wavefunction is propagated within the structure by means of a two-dimensional time-dependent Schr¨odinger solver, and results are shown for a single-qubit gate able to split the wavepacket. This investigation is part of a feasibility study carried out to identify the experimental requirements for the realization of basic quantum-computing gates.