A new self-filling mechanism of band gap in magnetically doped topological surface states: spin-flipping inelastic scattering

Abstract

We investigate the influence of in-plane spin-exchange interactions on a topological insulator (TI) surface doped with nanomagnets under the second perturbation theory. We propose a novel self-filling mechanism of the surface-state band gap. It is found that when the out-of-plane exchange coupling favors an energy gap around the Dirac point, the in-plane component tends to suppress the induced gap, and even fill it completely. Our theory is based on the spin-flipping inelastic scattering, which creates a complex structure of self-energy, effectively modifying the band gap by renormalizing the magnetic moment and chemical potential. We explicitly analyze the filling effect in the electronic dispersion relation and density of states for different scenarios set by systemic parameters. This self-filling effect induced by spin-exchange coupling itself opens new perspectives for understanding of various magnetically doping phenomena on the TI materials and is expected to mediate the controversy concerning the magnetically doping induced gap.