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

摘要

We introduce a new quantum transport formalism based on a map of a real3-dimensional lead-conductor-lead system into an effective 1-dimensionalsystem. The resulting effective 1D theory is an in principle exact formalism tocalculate the conductance. Besides being more efficient than the principallayers approach, it naturally leads to a 5-partitioned workbench (instead of 3)where each part of the device (the true central device, the ballistic and thenon-ballistic leads) is explicitely treated, allowing better physical insightinto the contact resistance mechanisms. Independently, we derive a generalizedFisher-Lee formula and a generalized Meir-Wingreen formula for the correlatedand uncorrelated conductance and current of the system where the initialrestrictions to ballistic leads are generalized to the case of resistivecontacts. We present an application to graphene nanoribbons.