Unconventional superconductivity mediated by nematic fluctuations in a multiorbital system: Application to doped FeSe

We analyze superconductivity in a multiorbital fermionic system near the onset of nematic order, using doped FeSe as an example. We associate nematicity with a spontaneous polarization between dxz and dyz orbitals (a Pomeranchuk-type order) and analyze the pairing mediated by soft nematic fluctuations. Such a pairing gives rise to a highly anisotropic gap function whose structure strongly varies with temperature and leads to strongly non-BCS behavior in thermodynamics, spectroscopy, and transport. We compute the specific heat and its directional variation with a magnetic field, magnetic susceptibility, density of states, tunneling conductance, Raman intensity, superfluid stiffness, and penetration depth, both without and with impurity scattering. For the latter, we also compute optical conductivity and the Tc variation. We find good agreement with existing data for FeSe_1-xS_x and FeSe_1-xTe_x and suggest new experiments.