Self-consistent layer-projected scissors operator for band structures of complex 2D van der Waals materials

We introduce a computationally efficient method to calculate the quasiparticle (QP) band structure of general van der Waals (vdW) heterostructures. A layer-projected scissors (LAPS) operator, which depends on the one-body density matrix, is added to the density functional theory (DFT) Hamiltonian. The LAPS operator corrects the band edges of the individual layers for self-energy effects (both intralayer and interlayer) and unphysical strain fields stemming from the use of model supercells. The LAPS operator is treated self-consistently whereby charge redistribution and interlayer hybridization occurring in response to the band energy corrections are properly accounted for. We present several examples illustrating both the qualitative and quantitative performance of the method, including MoS$_2$ films with up to 20 layers, bilayer MoS$_2$ in an electric field, lattice-matched MoS$_2$/WS$_2$ and MoSe$_2$/WSe$_2$ bilayers, and MoSe$_2$/WS$_2$ moir\'e structures. Our work opens the way for predictive modeling of electronic, optical, and topological properties of complex and experimentally relevant vdW materials.