Finite-temperature photoemission in the extended Falicov-Kimball model: a case study for Ta${}_2$NiSe${}_5$

Utilizing the unbiased time-dependent density-matrix renormalization group technique, we examine the photoemission spectra in the extended Falicov-Kimball model at zero and finite temperatures, particularly with regard to the excitonic insulator state most likely observed in the quasi-one-dimensional material Ta${}_2$NiSe${}_5$. Working with infinite boundary conditions, we are able to simulate all dynamical correlation functions directly in the thermodynamic limit. For model parameters best suited for Ta${}_2$NiSe${}_5$ the photoemission spectra show a weak but clearly visible two-peak structure, around the Fermi momenta $k\simeq \pm k_{\mathrm{F}}$, which suggests that Ta${}_2$NiSe${}_5$ develops an excitonic insulator of BCS-like type. At higher temperatures, the leakage of the conduction-electron band beyond the Fermi energy becomes distinct, which provides a possible explanation for the bare non-interacting band structure seen in time- and angle-resolved photoemission spectroscopy experiments.