We theoretically study the Josephson effect in a superconductor/normal metal/superconductor junction based on Kekul\'e patterned graphene. For Kekul\'e-O junctions, Fermi momentum-splitting Andreev reflection at interface can be induced by off-resonant circularly polarized light applied normal region, which results possible $\pi$-state. In contrast, for Kekul\'e-Y is strongly suppressed due to ...

Motivation. Novel carbon allotropes, with finite molecular structure, including spherical fullerenes are nowadays currently produced and investigated. These compounds have beautiful architectures and show unusual properties that are very promising for the development of nanotechnologies. The Kekulé structure count and permanent of the adjacency matrix are computed for these molecules. Method. A...

Robustness of zero-modes two-dimensional Dirac fermions is examined numerically for the honeycomb lattice in presence Kekulé bond ordering. The split n=0 Landau levels a magnetic field as well generated by topological defects ordering are shown to exhibit anomalous robustness against disorder when chiral symmetry respected.

Altan derivatives of polycyclic conjugated hydrocarbons were recently introduced and studied in theoretical organic chemistry. We now provide a generalization of the altan concept, applicable to any graph. Several earlier noticed topological properties of altan derivatives of polycyclic conjugated hydrocarbons are shown to be the properties of all altan derivatives of all graphs. Among these ar...

The anti-Kekul\'{e} number of a connected graph $G$ is the smallest edges whose deletion results in subgraph having no Kekul\'{e} structures (perfect matchings). As common generalization (conditional) matching preclusion and $G$, we introduce $s$-restricted as without perfect matchings such that each component has at least $s+1$ vertices. In this paper, first show conditional problem are NP-com...