  Highly unconventional behavior of the thermodynamic response functions has
been experimentally observed in a narrow gap semiconductor samarium hexaboride.
Motivated by these observations, we use renormalization group technique to
investigate many-body instabilities in the f-orbital narrow gap semiconductors
with band inversion in the limit of weak coupling. After projecting out the
double occupancy of the f-orbital states, we formulate a low-energy theory
describing the interacting particles in two hybridized electron- and hole-like
bands. The interactions are assumed to be weak and short-ranged. We take into
account the difference between the effective masses of the quasiparticles in
each band. Upon carrying out the renormalization group analysis we find that
there is only one stable fixed point corresponding to the excitonic instability
with time-reversal symmetry breaking for small enough mismatch between the
effective masses.
