  The picture of how a gap closes in a semiconductor has been radically
transformed by topological concepts. Instead of the gap closing and immediately
re-opening, topological arguments predict that, in the absence of inversion
symmetry, a metallic phase protected by Weyl nodes persists over a finite
interval of the tuning parameter (e.g. pressure $P$) . The gap re-appears when
the Weyl nodes mutually annihilate. We report evidence that Pb$_{1-x}$Sn$_x$Te
exhibits this topological metallic phase. Using pressure to tune the gap, we
have tracked the nucleation of a Fermi surface droplet that rapidly grows in
volume with $P$. In the metallic state we observe a large Berry curvature which
dominates the Hall effect. Moreover, a giant negative magnetoresistance is
observed in the insulating side of phase boundaries, in accord with \emph{ab
initio} calculations. The results confirm the existence of a topological
metallic phase over a finite pressure interval.
