Magic Number Theory of Superconducting Proximity Effects and Wigner Delay Times in Graphene-Like Molecules

Rakyta, P. and Alanazy, A. and Kormányos, A. and Tajkov, Z. and Kukucska, G. and Koltai, J. and Sangtarash, S. and Sadeghi, H. and Cserti, J. and Lambert, C.J. (2019) Magic Number Theory of Superconducting Proximity Effects and Wigner Delay Times in Graphene-Like Molecules. Journal of Physical Chemistry C, 123 (11). pp. 6812-6822. ISSN 1932-7447

Abstract

When a single molecule is connected to external electrodes by linker groups, the connectivity of the linkers to the molecular core can be controlled to atomic precision by appropriate chemical synthesis. Recently, the connectivity dependence of the electrical conductance and Seebeck coefficient of single molecules has been investigated both theoretically and experimentally. Here, we study the connectivity dependence of the Wigner delay time of single-molecule junctions and connectivity dependence of superconducting proximity effects, which occur when the external electrodes are replaced by superconductors. Although absolute values of transport properties depend on complex and often uncontrolled details of the coupling between the molecule and electrodes, we demonstrate that ratios of transport properties can be predicted using tables of "magic numbers," which capture the connectivity dependence of superconducting proximity effects and Wigner delay times within molecules. These numbers are calculated easily, without the need for large-scale computations. For normal-molecule-superconducting junctions, we find that the electrical conductance is proportional to the fourth power of their magic numbers, whereas for superconducting-molecule-superconducting junctions, the critical current is proportional to the square of their magic numbers. For more conventional normal-molecule-normal junctions, we demonstrate that delay time ratios can be obtained from products of magic number tables.