Schrödinger-Poisson calculations for scanning gate microscopy of quantum rings based on etched two-dimensional electron gas

We present a systematic numerical simulation of the scanning gate microscopy experiment as performed on a quantum ring etched out of InGaAs/InAlAs heterostructure containing two-dimensional electron gas (2DEG). The present simulation accounts for 2DEG deformation under the presence of the tip, for modification of the electron charge trapped at the semiconductor/vacuum interface, for polarization effects at the interface, for the image charges related to the presence of the metal tip and for the three-dimensional character of the confinement. Once the potential is established by self-consistence of the Schrodinger-Poisson scheme, the linear conductance is evaluated by solution of the quantum scattering problem with several subbands at the Fermi level. We find that the conductance is a slowly varying function of the tip position in accordance with the experimental data. We study the high-pass-filtered conductance maps, which generally exhibit concentric patterns outside the ring area, and radial features inside the ring for negative charge at the tip. Influence of the surface charge and potential imperfections on conductance maps are also discussed.