We study the origin of layer dependence in band structures of two-dimensional
materials. We find that the layer dependence, at the density functional theory
(DFT) level, is a result of quantum confinement and the non-linearity 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
