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

Conventional Aubry André 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. In the limit of large periods, our numerical results can be interpreted in the language of the phase-space trajectories. As a first step, we have derived analytically the energy dependence of the localization observed in numerical simulations of the original Aubry-André model with large periods. Our main finding¹ 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.

¹ Rajesh K. Malla and M. E. Raikh, Phys. Rev. B 97, 214209 (2018).