Are photoemission replica bands evidence of interfacial forward scattering?

In plain words

Photoemission shows faint copies of the FeSe bands shifted by the energy of a substrate vibration, read as strong electron-phonon coupling. Others argue the copies form when emitted electrons lose energy after leaving the sample.

Precise statement

Lee et al. (2014) observed replica bands offset by $\sim 100\,\mathrm{meV}$, interpreted as $q \sim 0$ electron-phonon coupling with $\mathrm{SrTiO_3}$ phonons; Li and Sawatzky (2018) proposed extrinsic energy loss of photoelectrons. Determine whether the replicas are intrinsic spectral weight of the FeSe electrons and, if so, the coupling constant they imply.

What would settle it

Comparison with probes free of photoelectron energy loss (tunneling spectroscopy, momentum-resolved electron energy-loss spectroscopy) and with photoemission on FeSe over substrates with different phonons at matched doping.

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