Magnetoelectronic and optical properties of a ${\mathrm{MoS}}_2$ monolayer

A generalized tight-binding model is utilized to study Landau-level spectra of monolayer molybdenum disulfide. The intrinsic spin-orbit coupling effectively gives rise to multiple splitting of Landau levels. With a close inspection of wave-function characteristics, these levels can be classified into specific groups in terms of their orbital, spin, and valley signatures. In the calculation of magnetoabsorption spectra, the physical origin of the optical selection rules is clearly resolved. In particular, crossings of absorption lines are available and serve as a unique feature of the spin-orbit coupling. Our numerical results clearly demonstrate the magnetic control of spin and valley charge carriers and provide a basis for future experiments.

Figure 1

(a) Low-energy bands at $B=0$ without SOC. Subbands are drawn along $k_x$, and the band edges are located at highly symmetric points $K^{\prime }$, $\Gamma$, and $K$. (b) Same plot as (a) but with SOC. The solid blue and purple curves represent the spin-up states in the vicinity of the $K$ and $K^{\prime }$ valley, respectively, while the dashed red and brown curves shows the spin-down states. The top view of the atomic structure is shown in the inset of (a) and the momentum space in the inset of (b).

Figure 2

(a) Conduction-band Landau states without SOC: The low-lying Landau levels as a function of $B$ and the Landau wave functions at $B=40$ T are shown in sublattices, where the $K$ and $K^{\prime }$ valley states are respectively colored blue and purple. In the wave-function plot, the width of the horizontal axis is 60 nm centered at the middle of the magnetic supercell. (b) Same plot as (a) but with SOC. The $K$ and $K^{\prime }$ valley states with spin up are colored blue and purple while those with spin down are colored red and brown, respectively.

Figure 3

Same plot as Fig. 2 but for the valence-band Landau states. Additionally, the $\Gamma$ valley states are colored green.

Figure 4

The magneto-optical absorption spectra at different $B$ for the cases (a) without SOC and (b) with SOC. The absorption rates are in arbitrary units and the spectra are offset for clarity. Different types of transitions are distinguished by colored triangles.

Figure 5

$B$-dependent absorption frequencies for the cases (a) without SOC and (b) with SOC. The symbol size is proportional to the peak intensity. In each type of transition, states involving the first three absorption lines are also indicated.