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

Abstract

We introduce a new quantum transport formalism based on a map of a real 3-dimensional lead-conductor-lead system into an effective 1-dimensional 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 5-partitioned workbench (instead of 3) where each part of the device (the true central device, the ballistic and the non-ballistic 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.

12 pages, 5 figures

References in corpus (4)

• A knitting algorithm for calculating Green functions in quantum systems
• Coherent electronic transport through graphene constrictions: sub-wavelength regime and optical analogies
• Optimal block-tridiagonalization of matrices for coherent charge transport
• Stroboscopic wavepacket description of non-equilibrium many-electron problems

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• Mesoscopic thermoelectric transport near zero transmission energies
• Pushing the limit of quantum transport simulations
• Scanning Gate Microscopy of Quantum Contacts Under Parallel Magnetic Field: Beating Patterns Between Spin-Split Transmission Peaks or Channel Openings