Instabilities of quadratic band crossing points

Using a functional renormalization-group approach, we study interaction-driven instabilities in quadratic band crossing point two-orbital models in two dimensions, extending a previous study of Sun et al. [Phys. Rev. Lett. 103, 046811 (2009)]. The wave-vector dependence of the Bloch eigenvectors of the free Hamiltonian causes interesting instabilities toward spin-nematic, quantum anomalous Hall, and quantum spin Hall states. In contrast with other known examples of interaction-driven topological insulators, in the system studied here, the quantum spin Hall state occurs at arbitrarily small interaction strength and for rather simple intraorbital and interorbital repulsions.