An investigation of the disorder potential of quantum point contacts via scanning gate microscopy and machine learning*

Scanning Gate Microscopy (SGM) is one of the scanning probe techniques where a charged tip perturbs an electron sea while changes in conductance are concomitantly measured. Under very strict conditions such as a sufficiently weak perturbation caused by a delta-shaped potential, the SGM signal shows some correspondence with the local density of states of the device. These conditions, however, are typically difficult to be met and the usefulness of the technique is often questionable. Here, however, we show that it is possible to extract usefull information from SGM measurements if one considers it an inverse problem in quantum mechanics and uses machine learning tools to solve it.

For this study, we used a quantum point contact (QPC) as a prototypical device patterned on an InAlAs/InGaAs/InAlAs quantum well. Shubnikov de-Haas measurements revealed a mobility of 7.4x10⁴ cm²/V.s, which implies a mean free path of only 1.2 um at 280 mK. A set of SGM images were taken at different side-gate voltages of the QPC and cellular neural networks and evolutionary seach were used to estimate the background potential that gives rise to such small mobility. For this, we used the Green's function approach to generate theoretical SGM images given different random potentials. Our theoretical approach produces SGM images 72 % correlated with the experimental ones and from this we observe the formation of charge puddles, their dynamics under different side-gate biases and the static alloy disorder potential. Statistical analysis show that fluctuations of the potential have an average cluster radius around 30 nm and a correlation length close to 5.8 nm, which is comparable to those found in other two-dimensional electron systems.