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In a recent experiment the superconducting gap of a single unit cell thickFeSe film on SrTiO$_3$ substrate is observed by scanning tunneling spectroscopyand angle-resolved photoemission spectroscopy. The value of the superconductinggap is much larger than that of the bulk FeSe under ambient pressure. In thispaper we study the effects of screening due to the ferroelectric phonons onCooper pairing. We conclude it can significantly enhance the energy scale ofCooper pairing and even change the pairing symmetry. Our results also raisesome concerns on whether phonons can be completely ignored for bulk iron-basedsuperconductors.

High $T_c$ superconductivity at the FeSe/SrTiO$_3$ Interface