The importance of antiferromagnetic fluctuations are widely acknowledged in most unconventional superconductors. In addition, cuprates and iron pnictides often exhibit unidirectional (nematic) electronic correlations, including stripe and orbital orders, whose fluctuations may also play a key role for electron pairing. However, these nematic correlations are intertwined with antiferromagnetic or charge orders, preventing us to identify the essential role of nematic fluctuations. This calls for new materials having only nematicity without competing or coexisting orders. Here we report systematic elastoresistance measurements in FeSe$_{1-x}$S$_{x}$ superconductors, which, unlike other iron-based families, exhibit an electronic nematic order without accompanying antiferromagnetic order. We find that the nematic transition temperature decreases with sulphur content $x$, whereas the nematic fluctuations are strongly enhanced. Near $xapprox0.17$, the nematic susceptibility diverges towards absolute zero, revealing a nematic quantum critical point. This highlights FeSe$_{1-x}$S$_{x}$ as a unique nonmagnetic system suitable for studying the impact of nematicity on superconductivity.
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