Density-waves instability and a skyrmion lattice on the surface of strong topological insulators

In this work we analyze the instability conditions for spin-density-wave (SDW) formation on the surface of strong topological insulators. We find that for a certain range of Fermi energies and strength of interactions the SDW state is favored compared to the unmagnetized and the uniform-magnetization states. We also find that the SDWs are of spiral nature and, for a certain range of parameters, a Skyrmion lattice may form on the surface. We show that this phase may have a nontrivial Chern number even in the absence of an external magnetic field.