Infrared evidence for strong $C_{3}$ symmetry breaking in 1$T$-TiSe$_{2}$

Abstract: The interplay between lattice and electron degrees of freedom gives rise to competing ordered states in quantum materials, which can lead to a series of subsequent symmetry breaking transitions. While the differences are often subtle, these phases can be distinguished by their remaining point group symmetries. Here, we use infrared optical spectroscopy to probe symmetry breaking at the charge density wave transition of 1$T$-TiSe$<em>{2}$. We uncover a previously unobserved splitting of a doubly degenerate $E_u$ optical phonon at $T</em>{\mathrm{CDW}}\approx$ 190 K that constitutes direct evidence for the breaking of three-fold rotational symmetry. Our finding rules out proposals where the CDW transition to a low temperature chiral or nematic phase takes place through an intermediary state that preserves three-fold symmetry. The energy difference between the two former $E_{u}$ partners can only be explained by large $C_{3}$ breaking distortions of the same order of magnitude as previously observed changes in bond lengths, suggesting that $C_{3}$ symmetry breaking plays a dominant role in the CDW transition. The linewidth of the single phonon mode above $T_{\mathrm{CDW}}$ could be consistent with a fluctuating state where three-fold symmetry is also broken.