Unconventional superconductivity near a nematic instability 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 associate nematicity with spontaneous polarization between d_xz and d_yz orbitals. We derive pairing interaction, mediated by soft nematic fluctuations, and show that it is attractive, and its strength depends on the position on the Fermi surface. As the consequence, right at the nematic quantum-critical point (QCP), superconducting gap opens up at T_c only at special points and extends into finite arcs at T < T_c. In between the arcs the Fermi surface remains intact. This leads to highly unconventional behavior of the specific heat, with no jump at T_c and seemingly finite offset at T = 0. We discuss gap structure and pairing symmetry away from a QCP and compare nematic and spin-fluctuation scenarios. We apply the results to FeSe_1−xS_x and FeSe_1−xTe_x.