Rashba interaction as an external Yang–Mills field applied to one-dimensional system

The Rashba interaction in the low-dimensional semiconductor systems, which plays an important role in the spintronics, can be regarded as an external Yang–Mills field. With this viewpoint, the gauge field in a one dimensional (1D)-ring in the presence of the Rashba interaction can be reduced into two independent U(1) fields through an SU(2) transformation, which can also be extended to arbitrary 1D Rashba system. As an instance, a two-arms spin interferometer with a quantum dot embedded in one of its arms is considered. By tuning the Rashba interaction, the oscillation of the spin polarization of the current is predicted. Another application is about the persistent spin current in a Rashba ring. Keep the SU(2) gauge field in mind, it is straightforward to find that the persistent spin current may result from the Rashba interaction.