Nonequilibrium dual-fermion approach to electronic transport in disordered nanostructures

First-principles transport modeling of disordered nanostructures commonly resorts to certain effective medium theory constructed with single-site methods. These methods are essentially approximations that account for the diffusive aspect of the problem, but missing the interference-induced long-range effects such as localization, which also plays an important role in the mesoscopic regime. In this work, we report a real-space implementation of the dual-fermion method in the nonequilibrium Keldysh formalism for correcting the transport coefficients given by single-site methods. A mapping between the Keldysh Green's function and its dual counterpart is established, and a diagrammatic perturbation technique is used in the dual space, whereby the long-range Cooperon is taken into account. When treated at the zeroth order, this theory reproduces the nonequilibrium coherent potential approximation. We require self-consistency on two aspects: the dual Green's function is solved consistently with its self-energy, and the medium Green's function must have its real-space diagonal equal to that of the local impurity. The method is applied to a quasi-one-dimensional hopping lattice which mimics a disordered transport structure. The numerically computed transmission coefficient shows quantitative agreement with the exact solution in the weak-localization regime, significantly correcting the single-site results. In addition, we find that the dual-fermion method leads to a power-law dependency of resistance on the channel length, instead of the classical Ohm's law, and the exponent is insensitive to disorder strengths. We also show that the negative magnetoresistance effect, a phenomenon associated with weak localization, is obtained by our numerical model when a perpendicular magnetic field is introduced. The method presented here paves the way for an ab initio atomistic implementation to simulate disordered quantum transport in real nanostructures.