The Zero-Voltage Conductance of Nanographenes: Simple Rules and Quantitative Estimates

Zero-dimensional graphenes, also called nanographenes (NGs), consist of fragments of graphene with a finite number of hexagons. NGs can be viewed as a subset of the polycyclic aromatic hydrocarbons (PAHs) that continue to attract chemists' attention. We developed a simple theory for the ballistic electron transport through NGs which combines elements of the electronic structure theory of graphene, intuitive methods for the calculation of the molecular conductance, and chemical concepts such as Kekule structures. This theory enables one to analyze the relation between the structure of NGs and their conductance. General formulas and rules for the zero-voltage conductance as a function of the contact positions are derived. These formulas and rules require at most simple paper and pencil calculations in applications to systems containing several tens of carbon atoms.