Origin of the charge density wave in 1$T$-TiSe${}_2$

All-electron ab initio calculations are used to study the microscopic origin of the charge density wave (CDW) in 1$T$-TiSe${}_2$. A purely electronic picture is ruled out as a possible scenario, indicating that the CDW transition in the present system is merely a structural phase transition. The CDW instability is the result of a symmetry lowering by electron correlations occurring with electron localization. Suppression of the CDW in pressurized and in Cu-intercalated 1$T$-TiSe${}_2$ is explained by a delocalization of the electrons, which weakens the correlations and counteracts the symmetry lowering.

Figure 1

(a) Illustration of the CDW instability in one of the two Se-Ti-Se slabs in the $2\times 2\times 2$ 1$T$-TiSe${}_2$ super-structure. Arrows indicate the atomic displacements associated with the CDW distortion. (b) Se-Ti plane, containing the Se-Ti bonds. (c) Charge density distribution ($e$/a.u.${}^3$) of valence electrons (Se $4p$ and Ti $3d$) in the Se-Ti plane defined in (b) in the undistorted structure. (d) Same as (c), but for electrons near the Fermi level ($E_F\pm 0.5$ eV).

Figure 2

(a) Energy surface of the CDW distortion from the LDA, GGA, and mBJ-LDA calculations at ambient pressure and the mBJ-LDA calculation under a pressure of 6 GPa. The ratio of the valence bandwidths from the GGA, LDA, and mBJ-LDA calculations with respect to that from the mBJ-LDA calculation is addressed in the inset. (b) Orbital polarization $(n_{ilm}-{\overline{n}}_{il})/{\overline{n}}_{il}$ of the valence electrons. $n_{ilm}$ is the occupation number of suborbital $m$ of orbital $l$ in atom $i$, and ${\overline{n}}_{il}$ is the average occupation number of orbital $l$ in atom $i$. Note that occupation numbers refer to the muffin-tin spheres only.

Figure 3

(a) Charge transfer (${10}^{-3}{e/\text{a.u.}}^3$) in the Se-Ti plane defined in Fig. 1b associated with the alteration of the exchange-correlation functional from mBJ-LDA to GGA. (b) Charge transfer in the Se-Ti plane caused by a pressure of 6 GPa from mBJ-LDA calculations.