Low-energy bands and optical properties of monolayer WS2

•Band gap of monolayer WS2 increases linearly with external electric field.•Landau levels of nanolayer WS2 are proportional to the magnetic field.•Difference in spin splitting energy at the K and K′ valleys in the conduction band is quite large.•A huge splitting energy was found in the valence band at high magnetic fields due to the Zeeman fields.•Maximum of absorption coefficient is 0.18×102 cm−1 at the photon energy of 1.591 eV. In this work, we investigate the low-energy bands of monolayer WS2 under external electric and magnetic fields using an effective low-energy Hamiltonian. Our calculations indicate that band gap of monolayer WS2 increases linearly with an external perpendicular electric field and when the electric field energy Δz is equal to the size of spin splitting, the band gap including spin–orbit interaction of the monolayer increases to its band gap as the case of without spin–orbit interaction. In the presence of the magnetic field, spin splitting energy in the conduction and the valence bands at the valleys depends strongly on the magnetic field. In this work, the optical properties of monolayer WS2 are also calculated by using the Ehrenreich–Cohen formula. Our estimation for the square of the interband matrix element for transitions near the K points is in good agreement with previous calculations.