  In several families of iron-based superconducting materials, a d-wave pairing
instability may compete with the leading s-wave instability. Here we show that
when both states have comparable free energies, superconducting and nematic
degrees of freedom are strongly coupled. While nematic order causes a sharp
non-analytic increase in $T_{c}$, nematic fluctuations can change the character
of the s-wave to d-wave transition, favoring an intermediate state that does
not break time-reversal symmetry but does break tetragonal symmetry. The
coupling between superconductivity and nematicity is also manifested in the
strong softening of the shear modulus across the superconducting transition.
Our results show that nematicity can be used as a diagnostic tool to search for
unconventional pairing states in iron pnictides and chalcogenides.
