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

TL;DR

This paper develops an effective 1D quantum transport formalism for resistive nanocontacts, providing more efficient conductance calculations and better physical insight into contact resistance mechanisms, with applications to graphene nanoribbons.

Contribution

It introduces a new 1D formalism for quantum transport in resistive contacts, extending existing formulas to non-ballistic leads and improving computational efficiency.

Findings

Effective 1D theory accurately models conductance in resistive nanocontacts.

Generalized formulas for conductance and current applicable to resistive, non-ballistic leads.

Application demonstrates the method's effectiveness on graphene nanoribbons.

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.