Magneto-optical properties of bilayer transition metal dichalcogenides

In transition metal dichalcogenides the spin-orbit interaction affects differently the conduction and valence band energies as functions of $k$ and the band gap is large. Consequently, when a perpendicular magnetic field $B$ is applied the conduction and valence band Landau levels are also different and this leads to a splitting of the interband optical absorption lines in both the absence and presence of an external electric field $E_{z}$. When $B$ and $E_{z}$ are present the peaks in the imaginary part of the Hall conductivity give two distinct contributions of opposite sign to the interband spectrum. The real part of the right- and left-handed interband conductivity, however, retains its two-peak structure but the peaks are shifted in energy and amplitude with respect to each other in contrast with graphene. The response of the intraband conductivity is significantly modified when the Fermi energy $E_{F}$ and the field $B$ are varied. Its optical spectral weight is found to increase with $E_{F}$ in contrast with the decrease observed in graphene. Further, the position and amplitude of the intraband response depends on the field $B$. The absorption peaks vary linearly with $B$ for all fields similar to bilayer graphene for low fields but in contrast with the high-field $\sqrt{B}$ dependence in it.