  We theoretically investigate the localization properties of a spin-orbit
coupled spin-1/2 particle moving in a one-dimensional quasiperiodic potential,
which can be experimentally implemented using cold atoms trapped in a
quasiperiodic optical lattice potential and external laser fields. We present
the phase diagram in the parameter space of the disorder strength and those
related to the spin-orbit coupling. The phase diagram is verified via
multifractal analysis of the atomic wavefunctions and the numerical simulation
of diffusion dynamics. We found that spin-orbit coupling can lead to the
spectra mixing (coexistence of extended and localized states) and the
appearance of mobility edges.
