Electronic transport of a large scale system studied by renormalized transfer matrix method: application to armchair graphene nanoribbons between quantum wires

TL;DR

This paper introduces a renormalized transfer matrix method (RTMM) to efficiently study electronic transport in large-scale 2D systems like armchair graphene nanoribbons, overcoming numerical instability issues of traditional methods.

Contribution

The paper develops RTMM with reduced computational complexity and demonstrates its application to large-scale graphene nanoribbons, revealing transport properties and metal-insulator transitions.

Findings

Conductance in pure AGR is superlinear with Fermi energy.

Conductance is linear with width and independent of length in pure AGR.

Disorder with long-range correlation induces a metal-insulator transition.

Abstract

Study on the electronic transport of a large scale two dimensional system by the transfer matrix method (TMM) based on the Sch\"{o}rdinger equation suffers from the numerical instability. To address this problem, we propose a renormalized transfer matrix method (RTMM) by setting up a set of linear equations from U times of multiplication of traditional transfer matrix (U=N/S}with N and S being the atom number of length and the transfer step), and smaller S is required for wider systems. Then we solve the above linear equations by Gauss elimination method and further optimize to reduce the computational complexity from O(U^3M^3) to O(UM^3), in which M is the atom number of the width. Applying RTMM, we study transport properties of large scale pure and long-range correlated disordered armchair graphene nanoribbon (AGR) (carbon atoms up to 10^6 for pure case) between quantum wire contacts. As for pure AGR, the conductance is superlinear with the Fermi energy and the conductance is linear with the width while independent of the length, showing characteristics of ballistic transport. As for disordered AGR with long-range correlation, there is metal-insulator transition induced by the correlation strength of disorder. It is straightforward to extend RTMM to investigate transport in large scale system with irregular structure.