Quadrupolar charge dynamics in the nonmagnetic FeSe$_{1-x}$S$_x$ superconductors

We use polarization-resolved electronic Raman spectroscopy to study charge dynamics in non-magnetic FeSe$_{1-x}$S$_x$ superconductor. We observe two features of the $XY$ quadrupole symmetry: a low-energy quasi-elastic peak (QEP) and an electronic continuum. The QEP exhibits critical enhancement upon cooling towards the structural transition at $T_S(x)$. Below $T_S(x)$, the QEP diminishes gradually, and a gap with temperature evolution reminiscent of a mean-field order parameter opens in the continuum. The intensity of the QEP develops with increasing sulfur doping $x$ and maximizes at $x\approx$ 0.15, while the gap magnitude decreases with the suppression of $T_S(x)$. We interpret the development of the gap in the quadrupole scattering channel as the formation of a stripe quadrupole order: a wave of quadrupole moment without charge or spin modulation.