The sensitive energy band structure and the spiral current in helical graphenes

Abstract

We theoretically investigate the electronic properties in helical graphenes of both the armchair and the zigzag edge types. The energy band structures, the quantum conductances and the microscopic currents are calculated by the tight-binding and Green’s function methods. The results indicate that the helical graphenes behave significantly different, but regular in many cases, physical characteristics which sensitively depend on the sizes and the edge types. With the width increasing, the zigzag-edge helical graphenes become metal quickly, while the armchair-edge ones transform alternately between semiconductors and metals and the bandgaps experience obviously periodic changes. The possible edge states can also be distinguished in the quantum conductances along the helical direction. The results of current distributions show that there are obvious current pathways at lower energies and that the presence of edge states accompanies with an inner ring current channel. This is a method to produce helical currents in the nanometer scale. The study of this kind of graphenes not only extends the knowledge of graphene-family nanomaterials, but also paves the way for realizing the nano-scale helical circuits with the prospective application in carbon-based integrated circuits such as inductors.