We study the consequences of an electron-phonon (e-ph) interaction that is strongly peaked in the forward scattering ( = q 0) direction in a two-dimensional superconductor using Migdal-Eliashberg theory. We find that strong forward scattering results in an enhanced T c that is linearly proportional to the strength of the dimensionless e-phcoupling constant l m in the weak coupling limit. This interaction also produces distinct replica bands in the single-particle spectral function, similar to those observed in recent angle-resolved photoemission experiments on FeSe monolayers on SrTiO 3 and BaTiO 3 substrates. By comparing our model to photoemission experiments, we infer an e-phcoupling strength that can provide a significant portion of the observed high T c in these systems.A flurry of scientific activities has been generated by the discovery of an enhanced superconductivity in FeSe monolayers grown on SrTiO 3 (STO) substrates [1-20]. On its own, bulk FeSe has a modest superconducting transition temperatureT 9 c K [21]; however, when a monolayer is grown on an STO substrate, T c is increased dramatically [1]. Most reported T c values cluster within 55-75 K, close to the boiling point of liquid nitrogen (77 K). (A surprisingly highT 107 c K has also been reported in in situ transport measurements [9].) This discovery has opened a pathway to high-T c superconductivity through interface engineering, which has already produced high-T c ʼs in systems such as FeSe on BaTiO 3 (BTO) [8] and FeTe -x 1 Se x on STO [22]. Determining the origin of the T c enhancement in these interface systems is critical. At the moment, proposals include charge transfer between the substrate and FeSe [2-4, 20], electric field [6] and strain effects due to the substrate [5, 8], and lattice related effects such as enhanced electron-phonon (e-ph) coupling in the FeSe layer [1,13,16] or across the interface [7,19]. Strong evidence for the latter has been provided by a recent angleresolved photoemission spectroscopy (ARPES) study [7], which observed replica bands in the single-particle spectral function of the FeSe monolayer. These replicas are interpreted as being produced by coupling between the FeSe d 3 electrons and an optical oxygen phonon branch in the STO substrate. Moreover, the replica bands are complete copies of the corresponding main bands, which implies that the responsible e-phinteraction is strongly peaked in the forward scattering direction (small momentum transfers). Such momentum dependence is notable because it can enhance superconductivity in most pairing channels [23][24][25][26][27][28][29][30][31]. As such, this crossinterface coupling provides at the same time a suitable mechanism for the T c enhancement in the FeSe/STO and FeSe/BTO systems [7,8].We explore this possibility here by examining the consequences of strong forward scattering in the e-phinteraction for superconductivity and the spectral properties of a two-dimensional system. By solving the momentum dependent Eliashberg equations, we show that a pronounced...