  We investigate the properties of oxygen-functionalized carbides of lanthanide
elements with the composition M2CO2 (M=Gd, Tb,Dy) that form two-dimensional
(2D) structures. Our ab initio calculations reveal that oxygen termination
turns M2C monolayers into semiconductors with two dynamically stable phases. Of
these, the energetically favored alpha-phase becomes ferroelectric, whereas the
beta-phase turns anti-ferroelectric. Applying in-plane biaxial strain may
transform one phase into the other, changes the ferroelectric polarization of
the alpha-phase in a linear fashion, and modifies the size and nature of the
fundamental band gap from direct to indirect. The structure with a direct band
gap exhibits in-plane isotropic electronic and optical properties. This
previously unexplored class of systems also exhibits excellent photon
absorption in the ultraviolet range.
