## Optimal curvilinear transport of a spin-polarized electron with Rashba and Dresselhaus spin-orbit coupling in a uniform magnetic field

### Abstract

The spin-polarized transport of an electron along a curved-one dimensional wire with Rashba and Dresselhaus spin-orbit couplings (SOCs) and a uniform perpendicular magnetic field is considered in this study. Here we analytically derived the appropriate eigenenergies and eigenvalues of the system and numerically determine the output transmission coefficients. Spin polarization, probability current density and conductance are then obtained using transfer matrix approach to examine the dependence of spin transport on the radius, R, of curved wire, on the external magnetic field, B, and on the SOCs strengths.From our results, we find the condition, B ≈ R^(1/3), at which there would be no spin switching regardless of the SOC strengths. A value of R beyond this condition will no longer have a spin reversal. Moreover, for a material with sufficiently strong SOCs, regardless of its type, the effect of the external magnetic field is reduced. The effective SOC strength follows the standard form equation of a circle in which the Rashba SOC and the Dresselhaus SOC are the component coordinates. From here, we optimize the probability current density by properly tuning the Rashba coupling strength for a given value of B, R and Dresselhaus SOC.