  Polar metals characterized by the simultaneous coexistence of ferroelectric
distortions and metallicity have attracted tremendous attention. Developing
such materials at low dimensions remains challenging since both conducting
electrons and reduced dimensions are supposed to quench ferroelectricity. Here,
based on first-principles calculations, we report the discovery of
ferroelectric behavior in two-dimensional (2D) metallic materials with
electrostatic doping, even though ferroelectricity is unconventional at the
atomic scale. We reveal that PbTe monolayer is intrinsic ferroelectrics with
pronounced out-of-plane electric polarization originated from its
non-centrosymmetric buckled structure. The ferroelectric distortions can be
preserved with carriers doping in the ferroelectric monolayer, which thus
enables the doped PbTe monolayer to act as a 2D polar metal. With an effective
Hamiltonian extracted from the parametrized energy space, we found that the
elastic-polar mode interaction is of great importance for the existence of
robust polar instability in the doped system. The application of this doping
strategy is not specific to the present crystal, but is rather general to other
2D ferroelectrics to bring about the fascinating metallic ferroelectric
properties. Our findings thus change conventional acknowledge in 2D materials
and will facilitate the development of multifunctional material in low
dimensions.
