Band structure and optical response of $2H\text{−}\mathrm{Mo}{X}_2$ compounds ($X=\mathrm{S}$, Se, and Te)

We report calculations of the electronic and optical properties for the $2H\text{−}\mathrm{Mo}{X}_2$ $(X=\mathrm{S},\mathrm{Se},\mathrm{Te})$ compounds using the full potential linear augmented plane wave method within the local density approximation. When S is replaced by Se and Te, the energy gap changes and the bandwidth of the $\mathrm{Mo}\text{−}d$ bands reduces. From the partial density of states we find a strong hybridization between $\mathrm{Mo}\text{−}d$ and $X\text{−}p$ states below the Fermi energy $E_F$. On going from S to Se to Te the structures in the frequency-dependent imaginary part of the dielectric function ${\epsilon }_2\left(\omega \right)$ shifts towards lower energies. The frequency-dependent reflectivity and absorption show that the plasma minimum also shifts towards lower energies. We compare our calculations with the experimental optical data and find a good agreement.

Figure 1

Band structure and total DOS (—) in states/eV unit cell, along with the partial DOS, where (∙ ∙ ∙) denotes chalcogen-$s$, (∙ ∙ ∙)), and (∙ ∙ ∙) Mo-$d$ states for $2H\text{−}\mathrm{Mo}{\mathrm{Se}}_2$ and $2H\text{−}\mathrm{Mo}{\mathrm{Te}}_2$. All the partial DOS are multiplied by 3.

Figure 2

Calculated ${\epsilon }_2^{\perp }\left(\omega \right)$ (—) and ${\epsilon }_2^{\Vert }\left(\omega \right)$ (—) along with the ${\epsilon }_2^{\perp }\left(\omega \right)$ experimental data (- - -) of Beal and Hughes (Ref. 14) for $2H\text{−}\mathrm{Mo}{\mathrm{Se}}_2$ and $2H\text{−}\mathrm{Mo}{\mathrm{Te}}_2$.

Figure 3

Calculated ${\epsilon }_1^{\perp }\left(\omega \right)$ (—) and ${\epsilon }_1^{\Vert }\left(\omega \right)$ (—) along with the ${\epsilon }_1^{\perp }\left(\omega \right)$ experimental data (∙ ∙ ∙) of Beal and Hughes (Ref. 14) for $2H\text{−}\mathrm{Mo}{\mathrm{Se}}_2$ and $2H\text{−}\mathrm{Mo}{\mathrm{Te}}_2$.

Figure 4

Calculated reflectivity spectrum (—) for $\vec{E}\perp \mathbf{c}$ along with the experimental data (Refs. 14, 17) (- - -) for $2H\text{−}\mathrm{Mo}{X}_2$ compounds.

Figure 5

Calculated absorption coefficient (—) for $\vec{E}\perp \mathbf{c}$ along with the experimental data (Ref. 14) (- - -) for the $2H\text{−}\mathrm{Mo}{X}_2$ compounds.