Magic ratios for connectivity-driven electrical conductance of graphene-like molecules

TL;DR

This paper introduces a new magic ratio rule (MRR) that predicts electrical conductance ratios of graphene-like molecules based on connectivity, validated by experiments and density functional theory calculations, highlighting the role of molecular connectivity in conductance.

Contribution

The paper presents the first connectivity-based magic ratio rule (MRR) for predicting conductance ratios in graphene-like molecules, combining experimental and theoretical validation.

Findings

The MRR accurately predicts conductance ratios based on connectivity.

Experimental and DFT calculations support the MRR's validity.

The MRR is exact in tight binding models and guides real molecule analysis.

Abstract

Experiments using a mechanically-controlled break junction and calculations based on density functional theory demonstrate a new magic ratio rule (MRR),which captures the contribution of connectivity to the electrical conductance of graphene-like aromatic molecules. When one electrode is connected to a site i and the other is connected to a site i' of a particular molecule, we assign the molecule a magic integer Mii'. Two molecules with the same aromatic core, but different pairs of electrode connection sites (i,i' and j,j' respectively) possess different magic integers Mii' and Mjj'. Based on connectivity alone, we predict that when the coupling to electrodes is weak and the Fermi energy of the electrodes lies close to the centre of the HOMO-LUMO gap, the ratio of their conductances is equal to (Mii' /Mjj')2. The MRR is exact for a tight binding representation of a molecule and a qualitative guide for real molecules.