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The recent observation of replica bands in single-layer FeSe/SrTiO$_3$ byangle-resolved photoemission spectroscopy (ARPES) has triggered intensediscussions concerning the potential influence of the FeSe electrons couplingwith substrate phonons on the superconducting transition temperature. Here weprovide strong evidence that the replica bands observed in the single-layerFeSe/SrTiO$_3$ system and several other cases are largely due to the energyloss processes of the escaping photoelectron, resulted from the well-knownstrong coupling of external propagating electrons to Fuchs-Kliewer (F-K)surface phonons in ionic materials in general. The photoelectron energy loss inARPES on single-layer FeSe/SrTiO$_3$ is calculated using the demonstratedsuccessful semi-classical dielectric theory in describing low energy electronenergy loss spectroscopy of ionic insulators. Our result shows that theobserved replica bands are mostly a result of extrinsic photoelectron energyloss and not a result of the electron phonon interaction of the Fe d electronswith the substrate phonons. The strong enhancement of the superconductingtransition temperature in these monolayers remains an open question.

Electron phonon coupling versus photoelectron energy loss at the origin of replica bands in photoemission of FeSe on SrTiO$_3$