  Since any realistic electronic device has some degree of disorder, predicting
disorder effects in quantum transport is a critical problem. Here we report the
theory of nonequilibrium coherent potential approximation (NECPA) for analyzing
disorder effects in nonequilibrium quantum transport of nanoelectronic devices.
The NECPA is formulated by contour ordered nonequilibrium Green's function
(NEGF) where the disorder average is carried out within the coherent potential
approximation on the complex-time contour. We have derived a set of new rules
that supplement the celebrated Langreth theorem and, as a whole, the
generalized Langreth rules allow us to derive NECPA equations for real time
Green's functions. The solution of NECPA equations provide the disorder
averaged nonequilibrium density matrix as well as other relevant quantities for
quantum transport calculations. We establish the excellent accuracy of NECPA by
comparing its results to brute force numerical calculations of disordered
tight-binding models. Moreover, the connection of NECPA equations which are
derived on the complex-time contour, to the nonequilibrium vertex correction
theory which is derived on the real-time axis, is made. As an application, we
demonstrate that NECPA can be combined with density functional theory to enable
analysis of nanoelectronic device physics from atomistic first principles.
