Theory of Temperature-dependent Collective Excitations in Excitonic Insulators

Semimetals with small gaps are predicted to be unstable against long-range Coulomb interaction that leads to an excitonic insulator state. However, an interaction-induced excitonic insulator state is indistinguishable from a charge density wave state that forms due to electron-phonon interactions from the symmetry perspective. Both mechanisms lead to energy gaps and spatial inhomogeneity. Motivated by a recent momentum-resolved electron energy-loss spectroscopy study of soft collective modes in the semimetal 1T-TiSe₂, we develop a time-dependent mean-field theory to study temperature-dependent collective excitations. The model includes both intraband and interband excitations, and direct and exchange interactions, and allows for the formation of exciton condensates at low temperatures. When the system does not support an exciton insulator state, thermally-excited plasmons are observed in intraband excitations while excitons are observed in interband excitations. When the condensates form, however, interband collective modes including Higgs modes and $2P$-like excitons are observed in both interband and intraband excitations even at low temperatures when plasmons are not formed. We then comment on the implications of our theory for the interpretation of the experimental observations.