  Intrinsic polar metals are rare, especially in oxides, because free electrons
screen electric fields in a metal and eliminate the internal dipoles that are
needed to break inversion symmetry. Here we use first-principles
high-throughput structure screening to predict a new polar metal in bulk and
thin film forms. After screening more than 1000 different crystal structures,
we find that ordered BiPbTi2O6 can crystallize in three polar and metallic
structures, which can be transformed between via pressure or strain. In a
heterostructure of layered BiPbTi2O6 and PbTiO3, multiple states with different
relative orientations of BiPbTi2O6 polar displacements, and PbTiO3
polarization, can be stabilized. At room temperature, the interfacial coupling
enables electric fields to first switch PbTiO3 polarization and subsequently
drive 180{\deg} change of BiPbTi2O6 polar displacements. At low temperatures,
the heterostructure provides a tunable tunnelling barrier and might be used in
multi-state memory devices.
