Exact solutions to the transportation of electrons through equilateral polygonal quantum rings with Rashba spin-orbit interaction

Abstract

The quantum transportation of electron through equilateral polygonal quantum rings with Rashba spin-orbit interaction is studied. By using the typical method of quantum network and the Landauer-Büttiker formalism, we solve analytically the scattering problem of electron through any equilateral polygonal quantum ring, and obtain the relevant formula for spin transportation conductance. The characters of conductance varying with wave-vector of electron and the strength of spin-orbit interaction are investigated, and the series of zero conductance points originating from spin-orbit interaction is determined. In the limit of infinite number of borders of equilateral polygon, we prove that the formula is consistent with the results obtained directly from the circular model of quantum rings.