Impact of clustering of substitutional impurities on quasiparticle lifetimes and localization

Motivated by the observation and prediction of clustering behavior for impurities substituted into the host lattice of a real material, and the dramatic impact this can have on electronic properties, we develop a simple approach to describe such an effect via the electron self-energy. We employ a disorder averaged T-matrix expansion taken to second order, which we modify to include a clustering probability parameter. This approach circumvents the need for specific cluster probability distributions, simplifying greatly the analysis of clustered impurities. To gain analytical insights, we study a nearest-neighbor square lattice tight-binding Hamiltonian with clustered impurity substitutions to investigate clustering of off-diagonal hopping impurities. We find that our T-matrix approach is in excellent agreement with exact numerical results from a tight-binding computation performed with the KWANT package. We observe a variety of interesting impurity clustering-induced effects in the self-energy such as the suppression of quasi-particle lifetimes at certain momenta and an increase in localization, as indicated by the inverse participation ratio. The KWANT results are reproduced in our modified T-matrix approach. In addition, our method allows for a full analytical treatment of clustering effects which can aid in physical insight.Comment: 8 pages, 6 figure

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.Comment: 15 pages, 12 figure