A method for finding the background potential of quantum devices from scanning gate microscopy data using machine learning

Abstract

The inverse problem of estimating the background potential from measurements of the local density of states (LDOS) is a challenging issue in quantum mechanics. Even harder is doing this estimation using approximate methods such as scanning gate microscopy (SGM). Here we propose a machine-learning-based solution by exploiting adaptive cellular neural networks (CNN). For the paradigmatic setting of a quantum point contact, the training data consist of potential-SGM functional relations represented by image pairs. These are generated by the recursive Green’s function method. We demonstrate that the CNN-based machine learning framework can predict the background potential corresponding to the experimental image data. This is affirmed by analyzing the estimated potential with image processing techniques based on the comparison between the charge densities and those obtained from different techniques. Correlation analysis of the images suggests the possibility of estimating different contributions to the background potential. In particular, our results indicate that both charge puddles and fixed impurities contribute to the spatial patterns found in the SGM data. Our work represents a timely contribution to the rapidly evolving field of exploiting machine learning to solve difficult problems in physics.

Reconstructing the potential configuration in a high-mobility semiconductor heterostructure with scanning gate microscopy

“…Another application which consists in using machine learning to adjust device parameters to compensate for uncontrolled disorder effects has been recently implemented in the case of a double quantum dot nanostructure [15]. It has also been suggested that properties of the disorder between the fingers of a QPC can be extracted from SGM data using cellular neural networks [16] or a swarming algorithm [17].…”