Modulation doping of the FeSe monolayer on SrTiO3

The discovery of higher-temperature superconductivity in FeSe monolayers on\nSrTiO$_3$ (STO) substrates has sparked a surge of interest in the interface\nsuperconductivity. One point of the agreement reached to date is that\nmodulation doping by impurities in the substrate is critical for the enhanced\nsuperconductivity. Remarkably, the universal doping of about 0.1 electrons per\nFe, \\textit{i.e.}, so-called ``magic'' doping, has been observed on a range of\nTi oxide substrates, which concludes that there likely is some important\ninteraction limiting the FeSe doping. Our study discovers that the polarization\nchange at the interface Se because of the close proximity to the substrate from\nthat in the free-standing FeSe film significantly amplifies the total potential\ndifference at the interface above and beyond the work function difference for\ncharge transfer. Additionally, the titanate substrate with a large number of\nfree electrons basically serves as an ``infinite'' charge reservoir, which\nleads to the saturated FeSe doping with the complete removal of interface\npotential gradient. Our work has developed the theory for modulation doping in\nthe Van der Waals materials/oxides heterostructure, providing a solution to the\npuzzle of ``magic'' doping in FeSe monolayers on titanates. The information\nalso presents experimental pathways to accommodate a variable carrier density\nof FeSe monolayers via modulation doping.\n