The superconductor at the LaAlO3-SrTiO3 interface provides a model system for the study of two-dimensional superconductivity in the dilute carrier density limit. Here we experimentally address the pairing mechanism in this superconductor. We extract
the electron-phonon spectral function from tunneling spectra and conclude, without ruling out contributions of further pairing channels, that electron-phonon mediated pairing is strong enough to account for the superconducting critical temperatures. Furthermore, we discuss the electron-phonon coupling in relation to the superconducting phase diagram. The electron-phonon spectral function is independent of the carrier density, except for a small part of the phase diagram in the underdoped region. The tunneling measurements reveal that the increase of the chemical potential with increasing carrier density levels off and is zero in the overdoped region of the phase diagram. This indicates that the additionally induced carriers do not populate the band that hosts the superconducting state and that the superconducting order parameter therefore is weakened by the presence of charge carriers in another band.
