THE GEOMETRICAL EFFECTS ON ELECTRONIC SPECTRUM AND PERSISTENT CURRENTS IN MESOSCOPIC POLYGON

Abstract

In this paper, a new mesoscopic polygon which possesses smooth transition at its corners is proposed. Because of the particularity of structure, this kind of mesoscopic polygon can also be a geometrical superlattice. The geometrical effects on the electron states and persistent current are investigated comprehensively in the presence of magnetic flux. We find that the particular geometric structure of the polygon induces an effective periodic potential which results in gaps in the energy spectrum. The changes of gaps show the consistency with the geometrical two-ness of this new polygon. This electronic structure and the corresponding physical properties are found to be periodic with period ϕ0 in the magnetic flux ϕ and can be controlled by the geometric method. We also consider the Rahsba spin-orbit interaction which double the energy levels splitting and leads to an additional small zigzag in one period of the persistent current. These new phenomena may be useful for the applications in quantum device design in the future.