Transport, Aharonov–Bohm, and Topological Effects in Graphene Molecular Junctions and Graphene Nanorings

Abstract

The unique ultrarelativistic, massless, nature of electron states in two-dimensional extended graphene sheets, brought about by the honeycomb lattice arrangement of carbon atoms in two dimensions, provides ingress to explorations of fundamental physical phenomena in graphene nanostructures. Here, we explore the emergence of new behavior of electrons in atomically precise segmented graphene nanoribbons (GNRs) and graphene rings with the use of tight-binding calculations, nonequilibrium Green’s function transport theory, and a newly developed Dirac continuum model that absorbs the valence-to-conductance energy gaps as position-dependent masses, including topological-in-origin mass barriers at the contacts between segments. Through transport investigations in variable-width segmented GNRs with armchair, zigzag, and mixed edge terminations, we uncover development of new Fabry–Pérot-like interference patterns in segmented GNRs, a crossover from the ultrarelativistic massless regime, characteristic of extended graphene systems, to a massive relativistic behavior in narrow armchair GNRs, and the emergence of nonrelativistic behavior in zigzag-terminated GNRs. Evaluation of the electronic states in a polygonal graphene nanoring under the influence of an applied magnetic field in the Aharonov–Bohm regime and their analysis with the use of a relativistic quantum field theoretical model unveils development of a topological-in-origin zero-energy soliton state and charge fractionization. These results provide a unifying framework for analysis of electronic states, coherent transport phenomena, and the interpretation of forthcoming experiments in segmented GNRs and polygonal rings.