Critical Role of the Exchange Interaction for the Electronic Structure and Charge-Density-Wave Formation in TiSe2

Abstract

We show that the inclusion of screened exchange via hybrid functionals provides a unified description of the electronic and vibrational properties of TiSe 2 . In contrast to local approximations in density functional theory, the explicit inclusion of exact, nonlocal exchange captures the effects of the electron-electron interaction needed to both separate the Ti-d states from the Se-p states and stabilize the charge-densitywave (CDW) (or low-T) phase through the formation of a p-d hybridized state. We further show that this leads to an enhanced electron-phonon coupling that can drive the transition even if a small gap opens in the high-T phase. Finally, we demonstrate that the hybrid functionals can generate a CDW phase where the electronic bands, the geometry, and the phonon frequencies are in agreement with experiments. DOI: 10.1103/PhysRevLett.119.176401 The charge density wave (CDW) instability is a common phenomenon in layered semimetallic transition metal dichalcogenides (TMDs) [1] and has attracted considerable interest over the years, from both the experimental and the theoretical side. The CDW phase is often found to compete with superconductivity and thus plays a similar role as the antiferromagnetic phase in strongly correlated heavy fermion systems or in high-T c cuprates [2][3][4][5]. This intriguing similarity has stimulated the search for a better understanding of the physical mechanism behind the CDW instability in TMDs [6].The CDW instability in TiSe 2 is one of the most studied and debated. On the experimental side, neutron diffraction [7] and x-ray scattering [8] have established the existence of a commensurate 2 × 2 × 2 structural transition at 200 K. This is confirmed by angle resolved photo emission spectroscopy (ARPES) as well as by transport measurements [7], where an abrupt increase in resistivity is found at the same temperature. However, upon further cooling the resistivity reaches an anomalous maximum [7], after which a weak metallic behavior is observed. By contrast, ARPES finds an insulating low-T phase, with a gap of approximately 0.15 eV [9][10][11][12][13][14]. In the high-T phase ARPES has not been able to conclude whether the system is semimetallic or semiconducting due to the very small indirect (possibly negative) gap. Theoretically, this fact makes TiSe 2 an ideal candidate to exhibit an excitonic insulator phase [9,[15][16][17] for which the CDW transition is driven by a purely electronic instability. Some recent experiments [18] partly support this scenario. On the other hand, excitonic correlations alone are insufficient as demonstrated in Ref. [19].Additional experimental evidence for the CDW instability has been provided by vibrational spectra as a function of temperature. A complete softening of an optical phonon at the L point has been observed in inelastic x-ray scattering experiments [20]. In Raman and infrared (IR) spectroscopy the transition is detected by the appearance of a large number of new modes [21,22], some of which can be related to the CDW transition ...

Orbital- and kz -Selective Hybridization of Se 4p and Ti 3d States in the Charge Densi

“…The resulting band dispersions ( Fig. 2(c)) show a structure similar to ab-initio calculations [7,33], where the three backfolded conduction bands split into a doublet (d 2 ) and singlet (d 1 ) branch at Γ * . The valence bands hybridise strongly only with the d 2 branch, while the d 1 branch remains unhybridised and is not pushed away from the Fermi level.…”

Ultrafast charge ordering by self-amplified exciton–phonon dynamics in TiSe2

“…We thus identify a selfamplified process from these observations: the decrease in the PLD → the decrease in the bandgap → the decrease in the energy of carriers → the further decrease in PLD. We expect such a dynamic interplay between electronic order and PLD, ignored in previous studies, would sustain in a variety of CDW materials such as NbSe 2 , TaS 2 , LaTe 3 , etc [89,97]. The results highlight the entangled dynamics between different degree of freedoms in quantum materials.…”

Excitonic effects in two-dimensional TiSe2 from hybrid density functional theory

“…We note that, in Ref. 36, it was found for the bulk material that the µ = 0 functional leads to the strongest enhancement of the electron-phonon couplings. This correlates with our observation that the µ = 0 limit gives the strongest excitonic effects.…”

“…The insulating character can be recovered with the DFT+U method, but the CDW is then lost as the gap opens [35]. A significant improvement was achieved by Hellgren et al, who successfully reproduced the insulating character and distortion for bulk TiSe 2 within hybrid density functional theory, although the gap in the CDW phase was found to be overestimated [36]. It is unclear to what extent to proposed interpretation, i.e.…”