  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.
