Determining band structure parameters of two-dimensional materials by deep learning

The field of two-dimensional materials has mastered the fabrication and characterisation of a broad range of novel high-quality compounds that feature increasing complexity. Determination of the band structure parameters of such complex materials is a major ingredient required for quantitative theory. This task currently presents a formidable challenge: ab initio methods often do not provide quantitatively accurate values of parameters, whereas inferring band structure parameters from experiments is hindered by the complexity of the band structure and indirect nature of experimental probes. In this work we propose a general framework for determination of band structure parameters from experimental data based on deep neural networks. As a specific example we apply our method to the penetration field capacitance measurement of trilayer graphene that effectively probes its density of states. First, we demonstrate that a trained deep network gives accurate predictions for the penetration field capacitance as a function of tight-binding parameters. Next, we use the fast and accurate predictions from the trained network to automatically determine tight-binding parameters directly from experimental data, with extracted parameters being in a good agreement with values in the literature. We conclude by discussing potential applications of our method to other materials and experimental techniques beyond penetration field capacitance.