Magnetic instability on the surface of topological insulators

Gapless surface states that are protected by time-reversal symmetry and charge conservation are among the manifestations of three-dimensional topological insulators. In this work we study how electron-electron interaction may lead to spontaneous breaking of time-reversal symmetry on surfaces of such insulators. We find that a critical interaction strength exists above which the surface is unstable with respect to the spontaneous formation of magnetization, and we study the dependence of this critical interaction strength on temperature and chemical potential.