Electronic and optical excitations of two-dimensional ZrS2 and HfS2 and their heterostructure

In a first-principles study based on density functional theory and many-body perturbation theory, we investigate the electronic properties and the optical excitations of ZrS2 and HfS2 monolayers and their van der Waals heterostructure. Both materials have an indirect quasiparticle band gap, which amounts to about 2.8 eV in ZrS(2 )and to 2.6 eV in HfS2. In both systems the valence-band maximum is at Gamma and the conduction-band minimum at M. Spin-orbit coupling induces a splitting of about 100 meV at the Gamma point in the valence band, while it does not affect the conduction band. The optical absorption spectra are dominated by excitonic peaks with binding energies between 0.6 and 0.8 eV. The ZrS2/HfS(2 )heterobilayer exhibits a peculiar type-I level alignment with a large degree of hybridization between the two monolayers in the valence band, while the conduction bands retain either ZrS(2 )or HfS2 character, respectively. As a consequence, both the electron and the hole components of the first exciton are localized in the ZrS2 monolayer with nonvanishing probability of finding the hole also in the HfS2 sheet.