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

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