Constrained-search density functional study of quantum transport in two-dimensional vertical heterostructures

Based on a microcanonical picture that maps the steady-state quantum transport process to a drain-to-source excitation, we develop a constrained-search density functional formalism for finite-bias quantum transport calculations. By variationally minimizing the total energy of an electrode-channel-electrode system without introducing separate bulk electrode information, ambiguities in identifying its nonequilibrium electronic structure under a bias is reduced and finite electrode cases can be naturally treated. We apply the approach to vertically stacked van der Waals heterostructures made of a hexagonal boron nitride (hBN) channel sandwiched by single-layer graphene electrodes, which so far could not be treated within first-principles calculations. We find that the experimentally observed negative differential resistance originates from the hBN defect-mediated hybridizations between two graphene states, and concurrently obtain a high-bias linear current increase that was not captured in previous semiclassical treatments. Going beyond the capability of existing $ab\ initio$ nonequilibrium quantum transport simulation methods, the developed formalism will provide valuable atomistic information in the development of next-generation nanodevices.