By systematic theoretical calculations, we have revealed an excitonic insulator (EI) in a van der Waals layered compound Ta$_2$Pd$_3$Te$_5$. First-principles calculations show that the monolayer is a nearly zero-gap semiconductor with the modified Becke-Johnson functional. Due to the like symmetry of the band-edge states, the 2D polarization $\alpha_{2D}$ would be finite as the band gap goes to zero, allowing for the EI state in the compound. Using the first-principles many-body perturbation theory, the $GW$-BSE calculation shows that the exciton binding energy $E_b$ is larger than the single particle band gap $E_g$, indicating the excitonic instability. Additionally, no structure instability is found in the phonon spectrum of this material. Our findings suggest that the Ta$_2$Pd$_3$Te$_5$ monolayer is an excitonic insulator without structure distortion.
Comment: 6 pages, 4 figures