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Whether vibrations of the substrate supply the rest is disputed.","posed_since":"2012","precise":"Monolayer FeSe/$\\mathrm{SrTiO_3}$(001) has only electron pockets at M (about 0.1 e per Fe), with a gap of $\\sim 15-20\\,\\mathrm{meV}$ that closes near $55-65\\,\\mathrm{K}$ in photoemission, while electron-doped FeSe without $\\mathrm{SrTiO_3}$ (K dosing, ionic gating) reaches $\\sim 40-48\\,\\mathrm{K}$. Determine the separate contributions to $T_c$ of electron doping, interfacial electron-phonon coupling to $\\mathrm{SrTiO_3}$ polar (Fuchs-Kliewer) phonons at $\\sim 80-100\\,\\mathrm{meV}$ through small-momentum forward scattering, and substrate screening.","problem_ref":"d36e1b4be6bb327bab375ec2d1f5b9dc572d46dc152cd470ef9ecf37bfba08c5","references":"","settled_by":"$T_{c}$ of monolayer FeSe at fixed doping on substrates with systematically varied polar-phonon coupling, compared with a quantitative pairing calculation.","status_note":"Inserting a metallic $\\mathrm{SrVO_3}$ layer that screens interfacial phonons lowered the pairing temperature to about 48 K (Guo et al., Nano Letters, 2024, arXiv 2407.09880), supporting a role for interfacial electron-phonon coupling.","title":"Why does $\\mathrm{SrTiO_3}$ raise the transition temperature of monolayer 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