Atomically thin two-dimensional (2D) materials host a rich set of electronic states that differ substantially from those of their bulk counterparts due to quantum confinement and enhanced many-body effects. This Topical Review focuses on the theory and computation of excitons, plasmons and quasiparticle band structures in 2D materials and their heterostructures. The general theory is illustrated by applications to various types of 2D materials including transition metal dichalcogenides, graphene, phosphorene, and hexagonal boron nitride. The weak and highly non-local dielectric function of atomically thin crystals is shown to be responsible for many of the unique properties exhibited by the 2D materials such as the formation of strongly bound, non-Hydrogenic excitons, large band gap renormalization effects, and the different signatures of excitons and plasmons in electron energy loss spectroscopy (EELS). Among other topics covered are spin-orbit coupling, trions, interlayer excitons, exciton dissociation, and environmental screening. Technical issues associated with the application of the many-body GW method and the Bethe-Salpeter equation (BSE) to 2D materials are also discussed. A combined quantum/classical method is introduced and used throughout to account for dielectric screening and self-energy effects from substrates and van der Waals heterostructures including the difficult case of non-matching lattices.
- 2D materials
- Density functional theory
- GW method
- van der Waals heterostructures