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 the nematic order with spontaneous polarization between d_xz and d_yz orbitals. 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 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 gives rise to highly unconventional behavior of the specific heat, with no jump at T_c  and an apparent finite offset at T=0, when extrapolated from a finite T. We argue that this behavior is consistent with the specific heat data for FeSe_1-xS_x near critical x for the onset of a nematic order.  We discuss the behavior of the gap away from a QCP and the pairing symmetry, and apply the results to FeSe_1-xS_x and FeSe_1-xTe_x, which both show superconducting behavior near the QCP distinct from that in a pure FeSe.