title: Magic ratios for connectivity-driven electrical conductance of graphene-like molecules.
abstract: Experiments using a mechanically controlled break junction and calculations based on density functional theory demonstrate a new magic ratio rule (MRR) that 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'. On the basis of connectivity alone, we predict that when the coupling to electrodes is weak and the Fermi energy of the electrodes lies close to the center 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.
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Yan
authors.initials: Y
authors.lastname: Geng
authors.affiliation: ‡Lancaster Quantum Technology Centre, Department of Physics, Lancaster University, Lancaster LA1 4YB, U.K.
authors.forename: Sara
authors.initials: S
authors.lastname: Sangtarash
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Cancan
authors.initials: C
authors.lastname: Huang
authors.affiliation: ‡Lancaster Quantum Technology Centre, Department of Physics, Lancaster University, Lancaster LA1 4YB, U.K.
authors.forename: Hatef
authors.initials: H
authors.lastname: Sadeghi
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Yongchun
authors.initials: Y
authors.lastname: Fu
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Wenjing
authors.initials: W
authors.lastname: Hong
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Thomas
authors.initials: T
authors.lastname: Wandlowski
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Silvio
authors.initials: S
authors.lastname: Decurtins
authors.affiliation: ‡Lancaster Quantum Technology Centre, Department of Physics, Lancaster University, Lancaster LA1 4YB, U.K.
authors.forename: Colin J
authors.initials: CJ
authors.lastname: Lambert
authors.affiliation: †Department of Chemistry and Biochemistry, University of Bern, Freiestrasse 3, CH-3012 Bern, Switzerland.
authors.forename: Shi-Xia
authors.initials: SX
authors.lastname: Liu