A Numerical Formulation to Calculate the Conductance of Mesoscopic Conductors Using Singular Value Decomposition

TL;DR

This paper introduces a novel numerical method using singular value decomposition to efficiently compute the conductance of complex mesoscopic conductors, demonstrated on graphene nanoribbons, with potential for large-scale atomic-level simulations.

Contribution

A new SVD-based formulation for calculating conductance in mesoscopic systems that simplifies handling complex structures and enhances scalability with parallel computing.

Findings

Effective in treating complicated atomic structures

Scalable to large systems with parallel computation

Applied successfully to graphene nanoribbons

Abstract

We present a new formulation to calculate the electric conductance of mesoscopic conductors by utilizing the singular value decomposition, which is a mathematical technique to manipulate matrices. Our formulation is useful in treating conductors with rather complicated atomic structures, for which naive recursion formula is cumbersome. It also has an advantage in scaling up the calculation by using parallel computation, which potentially allows us the real-scale calculations at the atomic level. On the other hands, the effects of electron-electron interactions are hard to be treated within this framework, since it depends crucially on the linearity of the system. In this paper, we study graphene nanoribbons with external leads for a simple example.