Generalized path integral method for Elliott-Yafet spin relaxations in quantum wells and narrow wires.

We generalized the semiclassical path integral method originally used in the D'yakonov-Perel' mechanism to study the spin relaxation of the Elliott-Yafet mechanism in low-dimensional systems. In quantum wells, the spin properties calculated by this method confirmed the experimental results. In two-dimensional narrow wires, size and impurity effects on the Elliott-Yafet relaxation were predicted, including the wire-width-dependent relaxation time, the polarization evolution on the sample boundaries, and the relaxation behavior during the diffusive-ballistic transition. These properties were compared with those of the D'yakonov-Perel' relaxation calculated under similar conditions. For ballistic narrow wires, we derived an exact relation between the Elliott-Yafet relaxation time and the wire width, which confirmed the above simulations.