Quantum transport through resistive nanocontacts: Effective one-dimensional theory and conductance formulas for nonballistic leads

We introduce a quantum transport formalism based on a map of a real three-dimensional lead-conductor-lead system into an effective one-dimensional (1D) system. The resulting effective 1D theory is an in principle exact formalism to calculate the conductance. Besides being more efficient than the principal layers approach, it naturally leads to a five-partitioned workbench (instead of three) where each part of the device (the true central device, the ballistic and the nonballistic leads) is explicitely treated, allowing better physical insight into the contact resistance mechanisms. Independently, we derive a generalized Fisher-Lee formula and a generalized Meir-Wingreen formula for the correlated and uncorrelated conductance and current of the system where the initial restrictions to ballistic leads are generalized to the case of resistive contacts. We present an application to graphene nanoribbons.