Theory of the Ferroaxial Charge Density Wave in 1T-TiSe$_2$

Recent experiments using strain to probe the charge-density wave (CDW) of 1T-TiSe$_2$ have uncovered additional transitions and broken symmetries inside the CDW state. The elastocaloric effect reveals a second transition below $T_\mathrm{CDW}$, which elastoresistivity shows to be associated with ferroaxial order, breaking all vertical mirror symmetries while preserving inversion. In addition, at even lower temperatures, a diverging nematic susceptibility has been reported through elastoresistivity. In this work, we argue that this rich phenomenology cannot be explained by the standard $L_1^-$ CDW order parameter, and instead requires the existence of a secondary CDW order parameter. Based on symmetry, microscopic, and diffraction considerations, we propose this subleading CDW to have $L_2^-$ symmetry. By analyzing the Landau theory of coupled $L_1^-$ and $L_2^-$ orders in the presence of strain, we reproduce the phase boundaries observed in the elastocaloric measurements and the emergence of ferroaxial order below the CDW transition. Moreover, the model supports a third threefold-rotational symmetry breaking transition at lower temperatures, consistent with the reported divergence of the nematic susceptibility.