Fig. 3: Broken ab-plane rotational symmetry.

a Resistances \({R}_{{xx}}\equiv\) \(\frac{{V}_{x}}{{I}_{x}}\) and \({R}_{{yy}}\equiv \frac{{V}_{y}}{{I}_{y}}\) of a ScV₆Sn₆ sample polished into a square plate. \({1.127R}_{{xx}}\) is used in the plot to account for a slight deviation from a perfect square-shape and misalignment of electrical contacts. \({1.127R}_{{xx}}\) and \({{{\rm{R}}}}_{{{\rm{yy}}}}\) trace each other almost perfectly when cooling down from \(150{{\rm{K}}}\), but develop a pronounced anisotropy below \({T}_{{CDW}}\). Such anisotropy decreases but doesn’t fully disappear when further cooling down below \({T}^{*}\). Inset: pictures of the square sample with illustrations of a-b and x-y axes as well as wire configurations. Curved arrows represent the expected current paths for \({I}_{x}\) and \({I}_{y}\) in the ab-plane. b Temperature trace of \({\frac{{R}_{{yy}}}{1.127R}}_{{{\rm{xx}}}}\) as a phenomenological parameter quantifying the ab-plane transport anisotropy. The largest anisotropy occurs between \({T}_{{CDW}}\) or \({T}^{*}\). c, Polar plots of optical polarization rotation measured at one location on the ab-plane and at various temperatures. The development of a four-leaf clover pattern with alternating “+” and “-” signs between \(95{{\rm{K}}}\) and \(85{{\rm{K}}}\) indicates intrinsic ab-plane anisotropy. The full scale of the polar plots is \(0.0005{{\rm{rad}}}\). The crossed blue lines represent fitted principal birefringent axes, which are close to the a-axis and its normal direction. Inset: image of the measured ScV₆Sn₆ single crystal with crystal axes labeled. Polarization rotation measurements at various locations are presented in Supplementary Fig. 4. d, e Depolarization effects revealed by comparing optical reflectivity (red) and the coherent reflection \({P}_{2}\) measured in the Sagnac interferometer (blue). \({P}_{2}\) measures the part of reflected optical power that remains coherent after reflection in a Sagnac interferometer, where depolarization effects in the sample, such as anisotropy and chirality, reduce such coherence. See Methods for details. Profoundly, cooling from \({T}_{{CDW}}\) to \({T}^{*}\), the reflectivity (red) shows a drop-plateau-drop while \({P}_{2}\) exhibits a single pronounced dip, revealing a large depolarization effect between \({T}_{{CDW}}\) and \({T}^{*}\), which is consistent with the observed transport and optical anisotropy. Cooling further below \({T}^{*}\), \({P}_{2}\) recovers from the dip and starts gradually to follow the trend of reflectivity, signaling the weakening and possible disappearance of the ab-plane anisotropy. \({P}_{2}\) measurements at various locations are presented in Supplementary Fig. 5. f, Schematics of polarization rotation setup based on a Wollaston prism that measures polarization rotation \({\theta }_{T}\) as a function of incident polarization \({{\rm{\alpha }}}\), which is achieved by rotating a half-wave plate (HWP) by \(\frac{{{\rm{\alpha }}}}{2}\).