MAGNETO-OPTICAL ABSORPTION COEFFICIENTS OF MONOLAYER MoSe2

We study the linear, third-order nonlinear, and total absorption coefficients (OACs) caused by intraand inter-band transitions in monolayer MoSe2 in the presence of a magnetic field by using the compact density matrix approach. The results show that the OACs display the blue-shift behaviour with an increase in the magnetic field. The Zeeman fields do not affect the peak positions but reduce peak intensities slightly. Besides, the strong spin-orbit coupling in monolayer MoSe2 causes the peaks to differ significantly due to spin-up and spin-down. The OACs due to intra-band transition display only one peak in the THz range, while the inter-band spectra show a series of peaks in the nearinfrared optical range, making monolayer MoSe2 a promising candidate for novel optoelectronic applications.

With their large natural bandgaps, the TMDCs resolve the gapless problem of graphene, gradually emerging as a potential candidate for new generation materials. That is why the TMCDs have attracted wide attention from scientists in recent years. Among them, monolayer molybdenum diselenide (MoSe2) has been studied increasingly due to its extraordinary properties [8]. MoSe2 has strong spin-orbit-coupling (SOC) with conduction band spin splitting of 0.184 eV and valence band spin splitting of -0.021 eV [9], which provides an excellent system for spin control [10]. In addition, the bandstructure of with () n x being the normalization oscillator functions, and the normalization constants are In the next subsection, we will use the above equations to evaluate the OACs.

Optical absorption coefficients
Using the compact density matrix approach, we calculate the linear and nonlinear optical susceptibilities for transitions between the two bands and ' as follows [6]: where h (3.35 Å) is the thickness of the MoSe2 monolayer [16]; c is the magnetic length; [6]; is the photon energy.
From the expressions for the optical susceptibilities shown in Eqs. (8) and (9), we can find the OACs as follows [17]: kk xx R I (11) here, 1,3 k for the linear and nonlinear terms;  is the permeability of the material;

Results and discussion
This section provides details for numerical evaluating the linear, nonlinear, and total OACs in monolayer MoSe2. The parameters are shown as they appear.
In Fig. 1 [12], WS2 [6], and phosphorene [11]. Since the SOC in monolayer MoSe2 is strong, the peak positions due to spin-up and spin-down are separated clearly with slightly higher energy for the spin-up case. Besides, the Zeeman field effect does not change the peak positions but reduces the peak intensities. This behaviour is consistent with that obtained in monolayer WS2 [6].
We now turn our attention to study the OACs due to inter-band transition.  It is clear that inter is proportional to (2n + 1), leading to the overlapped behaviour of the resonant peaks but gradually shifts to the higher-energy region with the increase of the Landau levels. That is the reason why the absorbed spectra appear in a series of peaks. For the peak positions, we see that int , 2, er s whose value is at the near-infrared region.
Besides, the peak intensities due to the inter-band transitions are much higher than those due to intra-band transitions. These results also agree well with those obtained in the monolayer WS2 [6] and MoS2 [12].
Like Fig. 5, Fig. 6 shows the OACs when dΔz = 51.25 meV. When the electric field is taken into account, the absorption spectra system shifts to the higher-energy region. This can be seen clearly from Eq. (13), which shows the absorbed photon energy is proportional to the electric field.
The influence of the magnetic field on the OACs due to inter-band transition is shown in Fig. 7. We can see that the peak positions shift to the higher-energy region because the cyclotron energy increases with the magnetic field. This result is consistent with that reported in the monolayer WS2 [6] and MoS2 [12].

Conclusion
We have studied the linear, third-order nonlinear,

Funding statement
Tran N. Bich is funded by Vingroup Joint Stock