  We consider the competition between the conventional s-wave and the triplet
Balian-Werthamer or the B-phase pairings in the doped three dimensional narrow
gap semiconductors, such as $\mathrm{Cu}_x\mathrm{Bi}_2\mathrm{Se}_3$ and
$\mathrm{Sn}_{1-x}\mathrm{In}_x\mathrm{Te}$. When the coupling constants of the
two contending channels are comparable, we find a simultaneously time-reversal
and parity violating $p + is$ state at low temperatures, which provides an
example of dynamic axionic state of matter. In contradistinction to the
time-reversal invariant, topological B-phase, the $p + is$ state possesses
gapped Majorana fermions as the surface Andreev bound states, which give rise
to an anomalous surface thermal Hall effect. The anomalous gravitational and
electrodynamic responses of the $p+is$ state can be described by the $\theta$
vacuum structure, where $\theta \neq 0$ or $\pi$.
