Electronic and vibrational properties of TiSe2 in the charge-density-wave phase from first principles

We study the charge-density-wave phase in TiSe2 by using first-principles density functional theory calculations with the harmonic approximation for the electron-phonon coupling. We consider several local functionals and both experimental and theoretical cell parameters. The results obtained are very sensitive to the cell parameters used. However, we show that, if the experimental cell is used, harmonic calculations are able to reproduce not only the structural instability of TiSe2 but also the effective distortion observed in the experiments, irrespective of the local functional used. If the experimental cell is used, the energy profile obtained by displacing the atoms is independent of the local functional considered too. With the semiempirical functional Grimme B97-D, aimed at describing better the van der Waals forces coupling the TiSe2 layers, the theoretical cell is in agreement with the experimental one and the structural analysis gives results analogous to the ones obtained with the experimental cell. We also present a study of the electronic structure evolution under the charge-density-wave deformation. In particular, we apply the unfolding technique in order to compare the calculated energy bands for the distorted structure with angle-resolved photoemission spectroscopy (ARPES) data taken at low temperature. In order to obtain a better agreement between ARPES and the calculated bands, both at high and low temperature, we investigate the effect of the correlation on the electrons of the localized Ti-3d orbitals by using the LDA+U method. We show that within this approximation the electronic bands for both the undistorted and distorted structure are in good agreement with ARPES. On the other hand, U eliminates the phonon instability of the system. A possible explanation for this counterintuitive result is proposed. Particularly, the possibility of taking into account the dependence of the parameter U on the atomic positions is suggested.