Applications Of Machine Learning In Quantum Transport

For the transport properties of mesoscopic system,disorder plays an important role in quantum spin Hall system,three-dimensional strong topological insulator and supercon-ductor,and fractional quantum Hall system.It can lead to metal insulator phase transition and drive topological phase transition.The concentration of impurity has a great influ-ence on the quantum transport.In some cases,small changes in disorder can significantly change the conductance.Therefore,it is necessary to carry out a large number of numerical calculations to study the influence of impurity energy and impurity concentration on the transport properties.In this paper,we hope to reduce the computing cost through popular machine learning technology.The feasibility of predicting the conductance of transport system with a large number of impurity points or adjustable impurity concentration by machine learning method is studied.In this paper,we mainly study the transport proper-ties of disordered two-dimensional materials and two applications of machine learning in quantum transport.First,we study the nature of the antidot-induced quantum percolation in quantum spin Hall insulators.The percolation threshold for different shapes and sizes is numerically studied using the tight-binding Hamiltonian.It is found that the percolation threshold p_csensitively depends on the length-width ratio for relatively small samples due to the finite size effect,while p_capproaches to a constant with the increase of sample size and becomes shape irrelevant.We also extend the discussion to whether the corner states exist in quantum spin Hall antidot systems.When the antidots density is close to the percolation threshold and the bulk gap is not closed,the longitudinal conductive channel provided by the helical edge state is destroyed,and a trend similar to the four higher-order corner states appears.Next,we study two applications of machine learning to the transport properties of dis-ordered two-dimensional materials.We build a fully connected neural network to provide a linear regression machine learning method for solving the two-dimensional nanostruc-ture electron quantum transport equation.The transmission coefficient of the disordered system is calculated to provide training and test data set for the neural network.The rep-resentation of the system encodes the energy and geometric information to represent the similarity between unordered configurations,while the mean square error(MSE)is used as a measure of similarity.The excellent performance of fully connected neural network model in capturing the complexity of interference phenomenon provides further support for its feasibility in dealing with the transport problem of disordered system.Another application is to analyze wave functions and determine their quantum phases.Here,we use the multilayer convolutional neural network to determine the quantum phase in the random electronic system.The convolution neural network can determine the phase of the wavefunction image of the system with unknown phase by training the neural network through supervised learning of the wavefunction image of the system with known phase.Convolutional neural network can correctly judge the phase of two-dimensional disor-dered topological system,that is,localized or delocalized,which proves the effectiveness of this method.