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We study the consequences of an electron-phonon ($e$-$ph$) interaction thatis strongly peaked in the forward scattering ($\mathbf{q} = 0$) direction in atwo-dimensional superconductor using Migdal-Eliashberg theory. We find thatstrong forward scattering results in an enhanced $T_c$ that is linearlyproportional to the strength of the dimensionless $e$-$ph$ coupling constant$\lambda_m$ in the weak coupling limit. This interaction also produces distinctreplica bands in the single-particle spectral function, similar to thoseobserved in recent angle-resolved photoemission experiments on FeSe monolayerson SrTiO$_3$ and BaTiO$_3$ substrates. By comparing our model to photoemissionexperiments, we infer an $e$-$ph$ coupling strength that can provide asignificant portion of the observed high $T_c$ in these systems.

Enhanced superconductivity due to forward scattering in FeSe thin films on SrTiO3 substrates