Free Electrons Holes and Novel Surface Polar Order in Tetragonal BaTiO3 Ground States

We find novel polar orders that yield electron (e-) and hole (h+) gas and depend on surface terminations, using density functional theory (DFT) that, unlike existing reports, relaxed all the ion positions of ATiO3 having spontaneous polarization Ps (A: alkali earth metal). By the experiments of atomic-oxygen cleaned surfaces of BaTiO3, we find both e- and h+ gas that are proven to originate from Ps and constrain electrostatic potential, which has been missing. These experiments that remarkably agree with the DFTs of defect free BaTiO3 reveal the properties of Ps-originated e-h+ and, for ferroelectric basics, an e-h+-posed intrinsic constraint on depolarization field arising from Ps in proper time ranges.