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

## TL;DR

This paper investigates the origin of layer dependence in the electronic band structures of 2D materials, attributing it to quantum confinement and exchange-correlation effects, and introduces an efficient computational scheme for multilayer systems.

## Contribution

It presents a novel method to derive multilayer band structures from monolayer calculations, significantly reducing computational effort.

## Key findings

- The layer dependence arises from quantum confinement and exchange-correlation non-linearity.
- The proposed scheme accurately reproduces multilayer band structures with less computational cost.
- It enables efficient GW calculations for complex multilayer 2D materials.

## Abstract

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 MoS$_2$, 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.