Electronic structure, magnetoexcitons and valley polarized electron gas in 2D crystals

Abstract: We describe here recent work on the electronic properties, magnetoexcitons and valley polarised electron gas in 2D crystals. Among 2D crystals, monolayer $MoS_2$ has attracted significant attention as a direct-gap 2D semiconductor analogue of graphene. The crystal structure of monolayer $MoS_2$ breaks inversion symmetry and results in K valley selection rules allowing to address individual valleys optically. Additionally, the band nesting near Q points is responsible for enhancing the optical response of $MoS_2$.We show that at low energies the electronic structure of $MoS_2$ is well approximated by the massive Dirac Fermion model. We focus on the effect of magnetic field on optical properties of $MoS_2$. We discuss the Landau level structure of massive Dirac fermions in the two non-equivalent valleys and resulting valley Zeeman splitting. The effects of electron-electron interaction on the valley Zeeman splitting and on the magneto-exciton spectrum are described. We show the changes in the absorption spectrum as the self-energy, electron-hole exchange and correlation effects are included. Finally, we describe the valley-polarised electron gas in $WS_2$ and its optical signature in finite magnetic fields.