Optical absorption and transmission in a molybdenum disulfide monolayer

Our recently proposed theoretical formulation [presented in D. Novko et al., Phys. Rev. B 93, 125413 (2016)] is used to study optical absorption and transmission in molybdenum disulfide $\left({\mathrm{MoS}}_2\right)$ monolayer as a function of incident photon energy and angle. The investigation is not focused on exploration of well-documented spin-orbit split excitons around optical absorption onset, but rather on the most intensive features in absorption spectrum in the visible and near-ultraviolet photon energy range $\left(1.7–4\mathrm{eV}\right)$. It is shown that three most intensive peaks, at 2.7, 3.1, and 3.7 eV, result from transitions between $\text{Mo}\left(d\right)$ and $\text{S}\left(p\right)$ valence and conduction bands and that the character of their charge/current density fluctuations is intrinsically in plane, located in the molybdenum plane. This also implies that ${\mathrm{MoS}}_2$ monolayer is completely transparent when illuminated by grazing incidence $p$-polarized light. The validity of the presented results is supported by our effective two-band tight-binding model and finally by good agreement with some recent experimental results.

Figure 1

Schematic description of the geometry of the system. The q2D crystal lies in the $x\text{−}y$ plane, $a$ represents lattice constant in the $x\text{−}y$ plane and $L_{uc}$ is the lattice constant in the $z$ direction. $\theta$ is incident angle of $s\left(\text{TE}\right)$ and $p\left(\text{TM}\right)$ polarized electromagnetic field.

Figure 2

The intensities of contributions of the $\text{Mo}\left(d\right)$ orbital (left panel) and $\text{S}\left(p\right)$ orbital (right panel) to ${\mathrm{MoS}}_2$ band structure.

Figure 3

A top view of ${\mathrm{MoS}}_2$ plane with molybdenum atoms (red) and sulfur atoms (blue). ${\mathbf{a}}_1$ and ${\mathbf{a}}_2$ are primitive vectors. Distance to the four alike neighbors is shown.

Figure 4

The valence band (violet) and conduction band (red) and their density of states (right panel). Notice the saddle points at $P,H$ and $M$ which give singular contribution to the density of states. The points $Q$ and $H$ are approximately at $(2\pi /3a,0)$ as noted in Ref. [32].

Figure 5

(a) The optical absorbance of $p$-polarized normal incidence $\left(\theta =0\right)$ light in ${\mathrm{MoS}}_2$-ML calculated from Eq. (11) (black solid line), the experimental result taken from Ref. [31] (blue dots). (b) Real part of optical conductivity (23) in units of ${\sigma }_0=e^2/4\hslash$ with increasing relaxation constant $\hslash \gamma =10\mathrm{meV}$ (turquoise), $30\mathrm{meV}$ (orange), $50\mathrm{meV}$ (red), and $100\mathrm{meV}$ (maroon). The inset shows the ab initio JDOS (turquoise) and TBA-JDOS (red).

Figure 6

Angle-resolved optical absorbance (a) and transmittance (b) in ${\mathrm{MoS}}_2$ monolayer (black lines) and in graphene monolayer (blue dashed lines). The incident angle increases as ${\theta }_n=n\mathrm{\Delta }\theta ;n=0,1,...,8$, where $\mathrm{\Delta }\theta ={10}^{\circ }$, as denoted in the graphs. Normal incidence $\left(\theta =0\right)$ absorbance in graphene taken from Ref. [18] (red dotted line) and Ref. [4] (green dashed-dotted line).