A General Algorithm For Determining The Conductivity Zeros In Large Molecular Nanostructures: Applications To Rectangular Graphene Sheets

TL;DR

This paper introduces a novel algorithm using inverse graph methods to identify conductance zeros in large molecular nanostructures like graphene sheets, aiding in understanding their electrical properties.

Contribution

It presents a new graphical inverse graph algorithm to determine conductance zeros in large molecular nanostructures, specifically applied to rectangular graphene sheets.

Findings

Identifies two types of Green's function zeros related to conductance cancellations.

Topological properties of inverse graphs determine the existence of conductance zeros.

Potential applications in designing nanostructures with specific electrical behaviors.

Abstract

We propose an algorithm for determining the zeros of the electric conductivity in large molecular nanonstructures such as graphene sheets. To this end, we employ the inverse graph method, whereby non-zeros of the Green's functions are represented graphically by a segment connecting two atomic sites, to visually signal the existence of a conductance zero as a line that is missing. In rectangular graphene structures the topological properties of the inverse graph determine the existence of two types of Green's function zeros that correspond to absolute conductance cancellations with distinct behavior in the presence of external disorder. We discuss these findings and their potential applications in some particular cases.