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By the first-principles electronic structure calculations, we have studiedelectronic structures of FeSe monolayer and bilayer thin films on SrTiO$_3$(001) with SrO-termination or TiO$_2$ termination. We find that both FeSemonolayer and bilayer on either termination behave like a slightly dopedsemiconductor and a collinear antiferromagnetic order on Fe ions. There is nosubstantial charge transfer between the FeSe layers and the substrate. FeSe isadhered to the SrTiO$_3$ surface by a dipole-dipole interaction. The Fermisurface is mainly the contribution of Fe-3d orbitals. A valence bandcontributed mainly by the O-$2p$ orbitals in the TiO$_2$ layer is locatedslightly below the Fermi level, which can become conducting upon a small dopingof holes.

Atomic and electronic structures of FeSe monolayer and bilayer thin films on SrTiO$_3$ (001): a first-principles study