Origin of layer dependence in band structures of two-dimensional materials

We study the origin of layer dependence in band structures of two-dimensional (2D) materials. We find that the layer dependence, at the density functional theory (DFT) level, is a result of quantum confinement and the nonlinearity of the exchange-correlation functional. We use this to develop an efficient scheme for performing DFT and $GW$ calculations of multilayer systems. We show that the DFT and quasiparticle band structures of a multilayer system can be derived from a single calculation on a monolayer of the material. We test this scheme on multilayers of MoS₂, graphene, and phosphorene. This new scheme yields results in excellent agreement with the standard methods at a fraction of the computation cost. This helps overcome the challenge of performing fully converged $GW$ calculations on multilayers of 2D materials, particularly in the case of transition-metal dichalcogenides, which involve very stringent convergence parameters.