  Ferroelectricity and metallicity are usually believed not to coexist because
conducting electrons would screen out static internal electric fields. In 1965,
Anderson and Blount proposed the concept of 'ferroelectric metal', however, it
is only until recently that very rare ferroelectric metals were reported. Here,
by combining high-throughput ab initio calculations and data-driven machine
learning method with new electronic orbital based descriptors, we
systematically investigated a large family (2,964) of two-dimensional (2D)
bimetal phosphates, and discovered 60 stable ferroelectrics with out-of-plane
polarization, including 16 ferroelectric metals and 44 ferroelectric
semiconductors that contain seven multiferroics. The ferroelectricity origins
from spontaneous symmetry breaking induced by the opposite displacements of
bimetal atoms, and the full-d-orbital coinage metal elements cause larger
displacements and polarization than other elements. For 2D ferroelectric
metals, the odd electrons per unit cell without spin polarization may lead to a
half-filled energy band around Fermi level and is responsible for the
metallicity. It is revealed that the conducting electrons mainly move on a
single-side surface of the 2D layer, while both the ionic and electric
contributions to polarization come from the other side and are vertical to the
above layer, thereby causing the coexistence of metallicity and
ferroelectricity. Van der Waals heterostructures based on ferroelectric metals
may enable the change of Schottky barrier height or the Schottky-Ohmic contact
type and induce a dramatic change of their vertical transport properties. Our
work greatly expands the family of 2D ferroelectric metals and will spur
further exploration of 2D ferroelectric metals.
