Impact of Electron-Hole Correlations on the $1T\text{−}{\mathrm{TiSe}}_2$ Electronic Structure

Several experiments have been performed on $1T\text{−}{\mathrm{TiSe}}_2$ in order to identify whether the electronic structure is semimetallic or semiconducting without reaching a consensus. In this Letter, we theoretically study the impact of electron-hole and electron-phonon correlations on the bare semimetallic and semiconducting electronic structure. The resulting electron spectral functions provide a direct comparison of both cases and demonstrate that $1T\text{−}{\mathrm{TiSe}}_2$ is of predominant semiconducting character with some spectral weight crossing the Fermi level.

Figure 1

Electron-hole susceptibilities as a function of energy for $\mathit{Q}=\mathbf{0}$. In blue, the susceptibilities result from a semimetal with a negative gap of $-50\mathrm{meV}$. In red, the calculation is done for a semiconductor with a positive gap of 50 meV. Solid lines are for $T^X$, the exciton condensation temperature. Dotted lines are for $T^L>T^X$, the temperature of the phonon softening (lattice instability). (a) Real and (b) imaginary part of the noninteracting susceptibility. (c) Real and (d) imaginary part of the interacting susceptibility.

Figure 2

(a)–(d) Electron spectral functions of the valence and conduction bands for semimetal and semiconductor scenarios calculated via the self-energies due to electron-phonon correlations. (e)–(h) Same as (a)–(d), but with the contribution of both electron-hole and electron-phonon correlations to the self-energies. (i)–(l) Electron spectral functions corresponding to (e)–(h) cut by the Fermi-Dirac function.

Figure 3

Phonon softening calculated in the semimetal (blue dots) and semiconductor (red dots) scenarios. These calculations are compared to measurements of Holt et al. [15] (open black circles) and Weber et al. [21] (green triangles).