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The observation of replica bands by angle-resolved photoemission spectroscopyhas ignited interest in the study of electron-phonon coupling at low carrierdensities, particularly in monolayer FeSe/SrTiO$_3$, where the appearance ofreplica bands has motivated theoretical work suggesting that the interfacialcoupling of electrons in the FeSe layer to optical phonons in the SrTiO$_3$substrate might contribute to the enhanced superconducting pairing temperature.Alternatively, it has also been recently proposed that such replica bands mightinstead originate from extrinsic final state losses associated with thephotoemission process. Here, we perform a quantitative examination of replicabands in monolayer FeSe/SrTiO$_3$, where we are able to conclusivelydemonstrate that the replica bands are indeed signatures of intrinsicelectron-boson coupling, and not associated with final state effects. Adetailed analysis of the energy splittings between the higher-order replicas,as well as other self-energy effects, allow us to determine that theinterfacial electron-phonon coupling in the system corresponds to a value of$\lambda = 0.19 \pm 0.02$.

Interfacial Electron-Phonon Coupling Constants Extracted from Intrinsic Replica Bands in Monolayer FeSe/SrTiO$_3$