Spin precession due to a non-Abelian spin-orbit gauge field

We study the spatial behavior of spin precession for traversing electrons in a two-dimensional system with both the Rashba and Dresselhaus spin-orbit (SO) couplings. Treating the two SO coupling as non-Abelian SO gauges and performing the unitary gauge transformation for the Hamiltonian, the effect of SO coupling is exactly represented by a spin-rotation operator providing a convenient framework for studying the property of ballistic spin transport. We derive the analytical expression for the spin configuration and demonstrate a classical analog of spin precession. The present approach provides a powerful means (e.g., the spin-rotation axis, the precession angle, and the cone angle) allowing concrete description of the local spin orientation. In particular, the spatial features such as the specific transport path with null spin precession and the special contour with complete cycles of spin precession can be easily identified.