Deep learning of deformation-dependent conductance in thin films: nanobubbles in graphene

Motivated by the ever-improving performance of deep learning techniques, we design a mixed input convolutional neural network approach to predict transport properties in deformed nanoscale materials using a height map of deformations (from scanning probe information) as input. We employ our approach to study electrical transport in a graphene nanoribbon deformed by a number of randomly positioned nano-bubbles. Our network is able to make conductance predictions valid to an average error of 4.3\%. We demonstrate that such low average errors are achieved by including additional inputs like energy in a highly redundant fashion, which allows predictions that are 30-40\% more accurate than conventional architectures. We demonstrate that the same method can learn to predict the valley-resolved conductance, with success specifically in identifying the energy at which inter-valley scattering becomes prominent. We demonstrate the robustness of the approach by testing the pre-trained network on samples with deformations differing in number and shape from the training data. We employ a graph theoretical analysis of the structure and outputs of the network and conclude that a tight-binding Hamiltonian is effectively encoded in the first layer of the network. We confirm our graph theoretical analysis numerically for different hopping processes in a trained network and find the result to be accurate within an error of 1\%. Our approach contributes a new theoretical understanding and a refined methodology to the application of deep learning for the determination transport properties based on real-space disorder information.