# Layer dependent electronic structure changes in transition metal dichalcogenides- The microscopic origin

## TL;DR

This study investigates how the electronic structure of transition metal dichalcogenides changes with layer thickness, revealing that interlayer hopping interactions primarily drive these changes, challenging the notion that van der Waals forces dominate.

## Contribution

The paper demonstrates that thickness-dependent electronic structure variations in MX₂ materials are mainly due to interlayer hopping, not changes in onsite energies or Madelung potential effects.

## Key findings

- Electronic structure changes up to 0.6 eV with thickness.
- Interlayer hopping interactions are the main cause of these changes.
- Onsite energy variations are negligible across different stacking configurations.

## Abstract

We have examined the electronic structure evolution in transition metal dichalcogenides MX$_2$, where M=Mo,W and X=S,Se and Te. These are generally referred to as van der Waals heterostructures on the one hand, yet one has band gap changes as large as 0.6 eV with thickness in some instances. This does not seem to be consistent with a description where the dominant interactions are van der Waals interactions. Mapping onto a tight binding model allows us to quantify the electronic structure changes which are found to be dictated solely by interlayer hopping interactions. Different environments that an atom encounters could change the Madelung potential and therefore the onsite energies. This could happen while going from monolayer to bilayer as well as in cases where the stackings are different from what is found in 2H structures. These effects are quantitatively found to be negligible, enabling us to quantify the thickness dependent electronic structure changes as arising from interlayer interactions alone.