  We have incorporated spin-orbit coupling into the Aubry-Andre model of
tight-binding electron motion in the presence of periodic potential with a
period incommensurate with lattice constant. This model is known to exhibit an
insulator-metal transition upon increasing the hopping amplitude. Without
external magnetic field, spin-orbit coupling leads to a simple renormalization
of the hopping amplitude. However, when the degeneracy of the on-site energies
is lifted by an external magnetic field, the interplay of Zeeman splitting and
spin-orbit coupling has a strong effect on the localization length. We studied
this interplay numerically by calculating the energy dependence of the Lyapunov
exponent in the insulating regime. Numerical results can be unambiguously
interpreted in the language of the phase-space trajectories. As a first step,
we have explained the plateau in the energy dependence of the localization
length in the original Aubry-Andre model. Our main finding is that a very weak
spin-orbit coupling leads to delocalization of states with energies smaller
than the Zeeman shift. The origin of the effect is the spin-orbit-induced
opening of new transport channels. We have also found that restructuring of the
phase-space trajectories, which takes place at certain energies in the
insulating regime, causes a singularity in the energy dependence of the
localization length.
