The crucial role of substrate in FeSe/STO: new insights to interface-driven superconductivity from first-principles

We investigate the superconducting properties of monolayer FeSe, both freestanding (ML FeSe) and on SrTiO$_3$ (STO), by simultaneously solving the Kohn-Sham Density Functional Theory and Bogoliubov--de Gennes equations. Our results demonstrate that the substrate profoundly alters both the normal-state and superconducting properties of FeSe. We identify proximity-induced superconductivity in the interfacial TiO$_2$ layer of STO, due to hybridization between Fe $d$ and O $p$ orbitals. This hybridization results in a fivefold increase in the superconducting gap width and confines superconducting states to the $M$ point in the Brillouin Zone. This is in contrast to ML FeSe, where superconductivity emerges at both the $\Gamma$ and $M$ points. Furthermore, the substrate modifies the orbital character of the states responsible for superconductivity, which change from Fe $d_{z^2}$ in ML FeSe to Fe $d_{xz}/d_{yz}$ in FeSe/STO. In both systems, we demonstrate an anisotropic superconducting gap with multiple coherence peaks, originating at different k-points in the Brillouin Zone. Additionally, in FeSe/STO, we identify emerging states unique to the superconducting phase arising from electron-hole hybridization at $M$, in agreement with experiments. Our findings highlight the decisive impact of substrate (hybridization, strain, charge transfer, magnetic order) on the superconducting properties of FeSe. We suggest potential pathways for engineering novel high-temperature FeSe-based superconductors by leveraging interfacial interactions in substrates with high electron affinity.