Three-dimensional momentum-resolved electronic structure of $1T\text{−}{\mathrm{TiSe}}_2:$ A combined soft-x-ray photoemission and density functional theory study

$1T\text{−}{\mathrm{TiSe}}_2$ is a quasi-two-dimensional transition metal dichalcogenide, which exhibits a charge density wave transition at a critical temperature of $\sim 200$ K as well as low-temperature superconductivity induced by pressure or intercalation. The electronic energy dispersion measured by soft x-ray angle-resolved photoemission is not only momentum resolved parallel to the surface but also perpendicular to it. Experiments are compared to density functional theory based band structure calculations using different exchange-correlation functionals. The results reveal the importance of including spin-orbit coupling for a good description of the experimental bands. Compared to calculations within the local density approximation, the use of the modified Becke-Johnson (mBJ) exchange functional leads to a band structure that does not need an artificial downwards shift of the valence band to fit the experiment. The mBJ functional thus clearly appears as the most adapted functional for the theoretical description of the $1T\text{−}{\mathrm{TiSe}}_2$ band structure within the DFT framework.

Figure 1

Band-structure calculations of the $(1\times 1\times 1)$ unreconstructed bulk unit cell of $1T\text{−}{\mathrm{TiSe}}_2$. (a) Comparison of the band structure along the $\mathrm{\Gamma }\mathrm{M}$ path obtained with the different exchange-correlation functionals. Dashed brown lines mark the effect of the mBJ exchange functional on the band gap, increasing the separation of occupied and unoccupied bands. (b) Full band structure calculated using LDA and mBJ exchange-correlation functionals, the latter with SO coupling.

Figure 2

$M^{\prime }\text{−}\mathrm{\Gamma }\text{−}M$ path. (Left) Measured data, region near $E_F$ intensified. (Center and right) Measurement with calculations superimposed, from left to right LDA, LDA + SO, mBJ + SO, respectively, the former ones being shifted down by $-0.3\mathrm{eV}$ to make the comparison easier.

Figure 3

$L^{\prime }\text{−}A\text{−}L$ path. (Left) Measured data. (Center and right) Measurement with calculations superimposed, from left to right LDA, LDA + SO, and mBJ + SO, respectively, LDA and LDA + SO again shifted downwards by $-0.3\mathrm{eV}$.

Figure 4

Measurement with a photon energy corresponding to a cut between $\mathrm{\Gamma }$ and $A$, compared with the LDA (blue) and mBJ + SO (green) calculations halfway between $\mathrm{\Gamma }$ and $A$. The LDA calculation is shifted downwards by $-0.3\mathrm{eV}$.