Additional is-wave Cooper pairing driven by nematic order in d-wave superconductors
We make a non-perturbative analysis of the strong interaction between gapless nodal fermions and nematic order parameter in two-dimensional $d_{x^2 - y^2}$ superconductors. We predict that the critical nematic fluctuation can generate a dynamical nodal gap if the fermion flavor $N$ is smaller than a threshold $N_c$. Such gap generation leads to an additional $is$-wave Cooper pairing instability, and induces a fully gapped $d_{x^2 - y^2} + is$ superconducting dome in the vicinity of nematic quantum critical point. The opening of dynamical gap has important consequences, including saturation of fermion velocity renormalization, weak confinement of fermions, and suppression of observable quantities.