Spin relaxation of two-dimensional electrons with a hierarchy of spin-orbit couplings

The density-matrix formalism is applied to calculate the spin-relaxation time for two-dimensional systems with a hierarchy of spin-orbit couplings, such as Rashba-type, Dresselhaus-type and strain-induced. It is found that the spin-relaxation time can be infinite if those coupling strengths alpha, beta, gamma(1) and gamma(2) satisfy either condition (i) alpha = beta, gamma(1) = 0 or (ii) alpha = -beta, gamma(2) = 0, which correspond to the vanishing Yang-Mills fields. The effect caused by the application of an external magnetic field is also discussed. It is found that the longitudinal spin component can possess infinite life time when the spin components, the Larmor precession frequency and the external magnetic field satisfy certain relations for which the Yang-Mills fields become zero.