Terahertz pulse-driven collective mode in the nematic superconducting state of Ba$_{1-x}$K$_x$Fe$_2$As$_2$

We investigate the iron-based superconductor Ba$_{1-x}$K$_x$Fe$_2$As$_2$ using intense terahertz (THz) light. In the superconducting state a THz Kerr signal is observed and assigned to non-linear THz coupling to superconducting degrees of freedom. The polarization dependence of the THz Kerr signal is remarkably sensitive to the coexistence of a nematic order. In the absence of nematic order the $C_4$ symmetric polarization dependence of the THz Kerr signal is consistent with a coupling to the Higgs amplitude mode of the superconducting condensate. In the coexisting nematic and superconducting state the signal becomes purely nematic with a vanishing $C_4$ symmetric component, signaling the emergence of a new superconducting collective mode activated by nematicity.