  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 $d\rightarrow d_{low} +$, with the "lower
critical dimension" $2< d_{low}<4$. Arguments for the existence of the quantum
critical point based on considerations in the large-$N$ limit in $d=3$, as well
as close to $d=2$, are given. In the one-loop calculation we find that $d_{low}
= 3.26$, and thus above, but not far from three dimensions. This translates
into a temperature/energy window $(T_c, T_*)$ over which the NFL scaling should
still be observable, before the Mott transition finally takes place at the
critical temperature $T_c \sim T_* \exp(-z C/(d_{low} -d)^{1/2})$. We estimate
$C=\pi/1.1$, dynamical critical exponent $z\approx 1.8$, and the temperature
scale $k_B T_* \approx (4 m/ m_{el} \epsilon^2)13.6 eV$, with $m$ as the band
mass and $\epsilon$ as the dielectric constant.
