Spin-orbit coupling in quasiperiodic systems

Electrons in incommensurate systems (e.g., electrons in a lattice in presence of a perpendicular magnetic field) have a rich behavior exemplified by the beautiful Hofstadter butterfly, a self-similar spectrum which is a multifractal Cantor set. We analyze the effect of spin-orbit coupling in this system which can be described by a generalization of Harper's equation. We find that the added term significantly modifies the scaling laws and appears to induce a delocalization of the insulator.