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Nematic order is ubiquitous in liquid crystals and is characterized by arotational symmetry breaking in an otherwise uniform liquid. Recently a similarphenomenon has been observed in some electronic phases of quantum materialsrelated to high temperature superconductivity, particularly in the Fe-basedsuperconductors. While several experiments have probed nematic fluctuations,they have been primarily restricted to the uniform nematic susceptibility, i.e.q = 0 fluctuations. Here, we investigate the behavior of finite-momentumnematic fluctuations by measuring transverse acoustic phonon modes withwavelengths of up to 25 unit cells in the prototypical Fe-based compoundBa(Fe$_{1-x}$Co$_x$)$_2$As$_2$. While the slope of the phonon dispersion givesinformation about the uniform nematic susceptibility, deviations from thislinear behavior at finite but small wave-vectors are attributed tofinite-momentum nematic fluctuations. Surprisingly, these non-zero qfluctuations lead to a softening of the phonon mode below the superconductingtransition temperature, in contrast to the behavior of the phonon velocity at q= 0, which increases below $T_c$. Our work not only establishes a sound methodto probe long wavelength nematic fluctuations, but also sheds light on theunique interplay between nematicity and superconductivity in Fe-basedcompounds.

Finite-momentum nematic fluctuations soften phonons in the superconducting state of Ba(Fe$_{1-x}$Co$_x$)$_2$As$_2$