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.

Transport properties in a multi-terminal regular polygonal quantum ring with Rashba spin—orbit coupling

“…For arbitrary two-terminal equilateral polygonal rings, an oscillation can be induced by the finite Rashba SOC effect. [29,31] For equilateral polygonal quantum rings with three terminals, it is demonstrated the Rashba SOC not only produces an oscillation in the amplitude but also introduces a distinct imbalance between the electron-transport probabilities of the two output leads, as it shows in Fig. 4 Thus, the conductance displays asymmetric features for the axisymmetric positions of the output leads.…”

“…Based on previous work, quantum transport of electrons through two terminals in arbitrary equilateral polygonal quantum rings with Rashba SOC was studied. [21,29,31] To the best of our knowledge, the effect of Rashba SOC on electron transport in multi-terminal regular polygonal quantum rings has not been investigated thoroughly. However, experimental studies [32] for multi-terminal quantum rings with magnetic fields have been reported.…”

Spin transport properties of a Dresselhaus-polygonal quantum ring

“…Beyond the work on circular ring models, [11][12][13][14] polygonal ring models with only RSOC have been reported in several studies. [15][16][17][18][19][20][21][22] Nevertheless, to the best of our knowledge, the effects of the DSOC on the spin transport in a polygonal ring have not been discussed, and it is now important to ask whether the time reversal symmetry (TRS) of the spin conductance of a polygon can be broken by the DSOC. It is also necessary to determine whether DSOC induces an anisotropic conductance and a shape-dependent conductance in a polygonal ring with RSOC.…”