  The origin of Cooper pairing in high-temperature superconductors, such as the
copper-oxide and iron-based system, is still under debate. High transition
temperatures together with unconventional pairing states support the picture of
an electronic pairing glue in the cuprates, where superconductivity is mediated
by collective bosonic excitations of the electron fluid. In other materials,
most importantly iron based systems with only hole or only electron pockets,
the microscopic origin is hotly debated. Scanning tunneling microscopy (STM)
has been shown to be a powerful experimental probe to detect electronic
excitations and further allows to deduce some fingerprints of bosonic
collective modes. Here, we demonstrate that the inclusion of inelastic tunnel
events is crucial for the interpretation of tunneling spectra and allows to
directly probe bosonic excitations via STM. We develop a model describing both
the elastic tunneling current, which displays the electronic spectral function,
and the inelastic current, that contains the information about the bosonic
spectrum, in the superconducting state. Adopting this extended tunneling
formalism we can naturally reproduce the tunneling spectra of various
unconventional superconductors and trace the occurring features back to an
opening of a spin gap in the superconducting state. More generally, our
approach is a strong argument in favour of a collective mode mediating the
pairing state in particular in iron-based systems. In particular, we conclude
that the debated pairing mechanism in LiFeSe is also of electronic origin with
sign-changing pairing symmetry.
