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We have incorporated spin-orbit coupling into the Aubry-Andre model oftight-binding electron motion in the presence of periodic potential with aperiod incommensurate with lattice constant. This model is known to exhibit aninsulator-metal transition upon increasing the hopping amplitude. Withoutexternal magnetic field, spin-orbit coupling leads to a simple renormalizationof the hopping amplitude. However, when the degeneracy of the on-site energiesis lifted by an external magnetic field, the interplay of Zeeman splitting andspin-orbit coupling has a strong effect on the localization length. We studiedthis interplay numerically by calculating the energy dependence of the Lyapunovexponent in the insulating regime. Numerical results can be unambiguouslyinterpreted in the language of the phase-space trajectories. As a first step,we have explained the plateau in the energy dependence of the localizationlength in the original Aubry-Andre model. Our main finding is that a very weakspin-orbit coupling leads to delocalization of states with energies smallerthan the Zeeman shift. The origin of the effect is the spin-orbit-inducedopening of new transport channels. We have also found that restructuring of thephase-space trajectories, which takes place at certain energies in theinsulating regime, causes a singularity in the energy dependence of thelocalization length.

Spinful Aubry-Andre model in a magnetic field: Delocalization facilitated by a weak spin-orbit coupling