Surface susceptibility and conductivity of ${\mathrm{MoS}}_2$ and ${\mathrm{WSe}}_2$ monolayers: A first-principles and ellipsometry characterization

We employ a recent formulation for the optical properties of two-dimensional crystals from first principles [L. Matthes et al., New J. Phys. 16, 105007 (2014); L. Matthes et al., Phys. Rev. B 94, 205408 (2016)] to compute the surface susceptibility and surface conductivity of ${\mathrm{MoS}}_2$ and ${\mathrm{WSe}}_2$ monolayers [G. Jayaswal et al., Opt. Lett. 43, 703 (2018)]. As electron-hole interactions are known to be crucial for the description of the absorption spectrum of monolayer transition metal dichalcogenides, the excitonic dielectric function is computed at the Bethe-Salpeter equation level, including spin-orbit interactions. For both of these examples, excellent agreement with experimental ellipsometry measurements is obtained. Driven by the emergence of additional features in our theoretical results, we applied a second-derivative analysis in order to identify excited exciton peaks in the ellipsometric spectra.

Figure 1

The computed LDA (gray) and $G_0{W}_0$ (blue, circles) band structure for the ${\mathrm{WSe}}_2$ monolayer.

Figure 2

A plot of the $\mathbf{k}$-point convergence for the ${\mathrm{A}}_{1s},{\mathrm{B}}_{1s}$, and ${\mathrm{C}}_{1s}$ peaks in the computed real and imaginary parts of the ${\mathrm{MoS}}_2$ dielectric function ${\varepsilon }_1$ and ${\varepsilon }_2$.

Figure 3

The convergence of the real and imaginary parts of the ${\mathrm{MoS}}_2$ dielectric function ${\varepsilon }_1$ and ${\varepsilon }_2$ as a function of the number of single particle states used to build the excitonic Hamiltonian.

Figure 4

A comparison of the surface susceptibilities and optical conductivities for monolayer ${\mathrm{MoS}}_2$ (a), (b) and the second derivative of the experimental results (c), (d). In (a) and (b), theoretical data is reported with solid lines and experimental data is reported with hollow circles.

Figure 5

A comparison of the surface susceptibilities and optical conductivities for monolayer ${\mathrm{WSe}}_2$ (a), (b) and the second derivative of the experimental results (c), (d). In (a) and (b), theoretical data is reported with solid lines and experimental data is reported with hollow circles.

Figure 6

Experimental ellipsometric parameter $\mathrm{\Psi }$ and $\mathrm{\Delta }$ for the single-layer ${\mathrm{WSe}}_2$.

Figure 7

Our single-layer ${\mathrm{WSe}}_2$ (hollow dots) versus the one reported in Ref. [31] (solid dots).