  We present a combined experimental and computational first-principles study
of the superionic and structural properties of CaF2 at high P-T conditions. We
observe an anomalous superionic behavior in the low-P fluorite phase that
consists in a decrease of the normal-> superionic critical temperature with
compression. This unexpected effect can be explained in terms of a P-induced
softening of a zone-boundary $X$ phonon which involves exclusively fluorine
displacements. Also we find that superionic conductivity is absent in the
high-P cotunnite phase. Instead, superionicity develops in a new low-symmetry
high-T phase that we identify as monoclinic (space group P2_1/c). We discuss
the possibility of observing these intriguing phenomena in related isomorphic
materials.
