Topological mott insulator in three-dimensional systems with quadratic band touching

We argue that a three-dimensional electronic system with the Fermi level at the quadratic band touching point such as HgTe could be unstable with respect to the spontaneous formation of the (topological) Mott insulator at arbitrary weak long-range Coulomb interaction. The mechanism of the instability can be understood as the collision of Abrikosov's non-Fermi liquid fixed point with another, quantum critical, fixed point, which approaches it in the coupling space as the system's dimensionality d→dlow+, with the "lower critical dimension" 2