Raman Optical Activity of 1T-TaS2

Measurements of optical activity can be readily performed in transparent matter by means of a rotation of transmitted light polarization. In the case of opaque bulk materials, such measurements cannot be performed, making it difficult to assess possible chiral properties. In this work, we present full angular polarization dependencies of the Raman modes of bulk 1T-TaS2, which has recently been suggested to have chiral properties after pulsed laser excitation. We found that a mechanical rotation of the sample does not alter polarization-resolved Raman spectra, which can only be explained by introducing an antisymmetric Raman tensor, frequently used to describe Raman optical activity (ROA). Raman spectra obtained under circularly polarized excitation demonstrate that 1T-TaS2 indeed shows ROA, providing strong evidence that 1T-TaS2 is chiral under the used conditions of laser excitation. Our results suggest that ROA may be used as a universal tool to study chiral properties of quantum materials.

: a) Schematic drawing of the experimental setup used to collect scattered light polarization dependent spectra. Polarizers I and II are set parallel to each other. Rotating the half-wave plate by θ/2 allowed for the detection of the polarization of scattered light rotated by θ in respect to the incident laser light polarization, which means that rotating the half-wave plate from 0 • to 180 • in respect to the polarizers' main axis allowed for detection of Raman spectra depending on the scattered light polarization angles from 0 • to 360 • . Coand cross-polarization configuration correspond to the alignment of the half-wave plate at 0 • (θ co =0 • ) and 45 • (θ cross =90 • ), respectively. b) Schematic drawing of the experimental setup used to collect Raman spectra corresponding to the sample rotation experiment. The setup yielded the expected results in case of silicon crystal, as shown in Fig. S3. Figure S2: Schematic drawing of the experimental setup used to collect Raman spectra measured in circularly polarized light (incident and scattered). The quarter-wave plate is set with its fast axis rotated by ±45 • in regard to the laser's linear polarization axis. Figure S3: Angular intensity plot of silicon 520 cm −1 Raman mode in sample rotation configuration: a) experiment data with a fitted function, b) model.

Room temperature measurements
Raman spectra dependent on the scattered light polarization rotation obtained at room temperature are shown in Fig S4. As can be seen, some lines originating from ordered domains in the crystal lattice are visible. The most intense line at 241 cm −1 is already linearly polarized, which indicates that arranged parts of the structure exhibit polarizationdependent properties in the NCCDW phase. Figure S4: a) Room temperature bulk 1T-TaS 2 Raman scattering spectra measured in scattered light polarization rotation configuration under 532 nm wavelenght excitation. b) -d) Angular intensity plots of three most pronounced lines at 74, 241 and 305 cm −1 with the fitted function: I = A + Bcos 2 (θ − θ max ). Low energy modes (below 72 cm −1 ) are attenuated by the Raman filter.

Raman tensors and angular dependencies
Raman tensors of A g and E g modes for C 3i symmetry point group are given by [1]: Based on the semi-classical model, the Raman mode intensity I can be written as [2]: where e i and e s stand for incident and scattered light electric field unit vector, respectively, and R is Raman tensor for given mode. Superscript t of e s denotes the transformation from a column vector to a row vector.
In case of scattered light polarization dependent measurements, the incident light polarization angle is fixed, and we can write e i = (cos θ 0 , sin θ 0 , 0), where θ 0 is a constant angle between the incident light polarization direction and the crystal's axis. e s depends on the angle set on the halfwave plate θ/2, which is changed during the experiment, and can be written as: e s = (cos(θ 0 +θ),sin(θ 0 +θ), 0). Applying Raman tensor for each Raman mode gives: Modelled angular dependencies for scattered light polarization rotation are shown in Fig   S5. Figure S5: Modelled A g and E g Raman modes angular intensity plots dependent on the scattered light polarization rotation for the sample rotated by 30 • for crystal with C 3i point group. A g modes stay the same, while E g modes' main axis rotates significantly (by 60 • ).
In sample rotation experiment θ 0 is changed during the measurements thus e i and e s can be written as: e i =e s =(cos θ 0 , sin θ 0 , 0). This results in Raman modes intensities (dependent on the θ 0 value): Modelled angular dependencies for sample rotation case are shown in Fig. S6. Figure S6: Angular intensity plot of A g and E g modes for crystal with C 3i symmetry point group in sample rotation configuration.