First principles simulation of electron transport in large-scale heterogeneous material by machine learning

There is a lack of efficient first principles method to calculate the electron transport in large-scale heterogeneous material with both phonon and defect/disorder scatterings.     Here we present a machine-learning Hamiltonian (ML-H) framework to fill this gap. Specifically, we train equivariant graph neural networks using DFT data to (i) create force field for large-scale MD and (ii) predict the electronic Hamiltonian for each MD snapshot. Ensemble average of the band structure gives the spectral function, which is then used in Kubo-Greenwood equation to obtain the conductivity. We apply this method to study the electrical conductivity of Cu films with different surface orientations, revealing their order and the underlying physical factors that determine this order.  This data-driven Hamiltonian route provides an efficient and transferable approach to calculate the electron transport in large-scale heterogeneous material, and offer insights into the design of metallic interconnects for micoelectronic applications.