Unconventional superconductivity mediated by nematic fluctuations in a multi-orbital system

We analyze superconductivity in a multi-orbital fermionic system near the onset of a nematic order, using doped FeSe as an example. We derive the pairing interaction, mediated by soft nematic fluctuations, and show that it is attractive, and that its strength depends on the position on the Fermi surface. As a consequence, right at the nematic quantum-critical point (QCP), the superconducting gap opens up only at special points and extends into finite arcs at. In between the arcs the Fermi surface remains intact. To characterize the fingerprints of this highly exotic and anisotropic gap structure, we compute a handful of measurable quantities, like specific heat, Knight shift, tunneling conductance, field induced modulation of the density of states and Raman intensity. We find a highly unconventional behavior of all of thermodynamic, spectroscopic and transport properties. For example, the specific heat shows no jump at the superconducting transition point and sets to an apparent finite offset at low temperature, when extrapolated from a finite temperature. We also study the effect of disorder. We find that with increasing impurity scattering, transition temperature decreases, and the gap structure becomes more isotropic.