Several strongly correlated electronic materials, such as FeSe, are thought to manifest quantum
critical transitions to an electronic nematic state. In my talk, I will discuss an interesting feature
of the nematic QCP: its anisotropic (quadrupolar) nature implies the appearance of dynamical
fluctuations at finite frequencies but very long spatial scales. These fluctuations encode information
on the driving mechanism of the nematic transition: whether it involves an external degree of
freedom, such as spin fluctuations, coupled to the electronic charge, or internal charge degrees of
freedom (a Pomeranchuk instability). I will show that Raman data for FeSe1-xSx agrees with the
hypothesis of a Pomeranchuk instability. Finally, I will also describe how these nematic critical
fluctuations are ‘shaped’ by conservation laws (which are constraints on long spatial scales),
implying a fascinating interplay between classical and quantum scales.
