Titanium diselenide (TiSe₂) is described as an excitonic insulator that exhibits a chiral charge density wave (CDW) phase. This is based in part on pump-probe measurements that have observed non-thermal melting of the CDW phase and chiral optical transitions in the CDW phase. The microscopic origin of this finite chirality remains an open question since the CDW structure is centrosymmetric and non-thermal melting of the CDW phase alone does not provide sufficient evidence for the condensation of excitons.

Using a combination of pump-probe measurements and first-principles calculations we show the non-thermal melting of the CDW and the chiral optical transitions can be understood without invoking the role of excitons. We uncover two distinct structures that can coexist in the CDW phase of TiSe₂. One is the (2x2x2) centrosymmetric structure and a second is a (2x2x1) non-centrosymmetric reconstruction. We show the nonthermal melting of the CDW phase can be understood by accounting for the impact of an elevated electronic temperature on the atomic atomic structure of the CDW. Finally, we calculate the circular polarization of optical transitions for the two CDW structures and compare with the degree of chirality determined from our pump probe studies.