  Iron selenide (FeSe) is an iron-based superconductor which shows unique
properties, including strongly anisotropic superconducting gap, paramagnetism
in undoped compound and extremely small Fermi pocket size. In this work, we
demonstrate that the sizes of electron and hole pockets in FeSe monolayer
become much smaller than those in bulk. The Fermi energy is in the order of a
few meV and can be fine-tuned by the thickness of graphene layers underneath.
Despite the low carrier density, the FeSe monolayers grown on trilayer or
multi-layer graphene are superconducting. The superconducting gap size is
sensitive to the Fermi energy of the hole band. Remarkably, the FeSe monolayer
provides the opportunity to study the physics in the crossover regime where the
Fermi energy and superconducting gap are comparable to each other.
