Magneto-optical transport properties of monolayer transition metal dichalcogenides

We study the optical transport properties of the monolayer transition metal dichalcogenides (TMDCs) such as ${\mathrm{MoS}}_{2}$, ${\mathrm{WS}}_{2}$, ${\mathrm{MoSe}}_{2}$, and ${\mathrm{WSe}}_{2}$ in the presence of a magnetic field. The TMDCs band structures are obtained and discussed by using the effective massive Dirac model, in which the spin and valley Zeeman effects as well as an external electric field are included. The magneto-optical absorption coefficient (MOAC) is derived as a function of absorbed photon energy when the carriers are scattered by random impurities combined with the intrinsic acoustic and optical phonons in TMDCs and the surface optical (SO) phonons of substrates. Our result shows that the spin-splitting feature appeared in all four TMDC materials. The combination of strong spin-orbit coupling (SOC) and Zeeman fields has doubled the Landau levels but has not changed the energy gap of the TMDCs monolayer, which can be controlled by the electric field. Because of their strong SOC effect, the absorption spectrum in monolayer TMDCs is separated into two separate peaks caused by spin up and down. At the low temperature, the MOAC intensity via impurity scattering is the biggest followed by that of the SO phonons while the intrinsic acoustic and optical phonon scatterings display the smallest. For the monolayer TMDCs on substrates, ${\mathrm{SiO}}_{2}$ always shows its superiority in comparison with the others. Among the four TMDC materials, ${\mathrm{MoSe}}_{2}$ shows the biggest MOAC intensity, while ${\mathrm{WS}}_{2}$ has the biggest value of the absorbed photon energy. The full-width at half-maximum (FWHM) via impurity scattering achieves its highest value in ${\mathrm{WS}}_{2}$, while this occurs in ${\mathrm{MoSe}}_{2}$ and ${\mathrm{MoS}}_{2}$ via intrinsic acoustic and optical phonon scatterings, respectively. Our estimation of mobility from FWHM gives good agreement with the experimental results in ${\mathrm{WS}}_{2}$.