[Paper Review] Layer dependent electronic structure changes in transition metal dichalcogenides- The role of geometric confinement

Ruma Das, Shishir Kumar Pandey+1 more|arXiv (Cornell University)|Feb 15, 2017

2D Materials and Applications1 references3 citations

TL;DR

This study challenges the prevailing view that geometric confinement dominates electronic structure changes in transition metal dichalcogenides (TMDs) with varying layer thickness. By mapping the system onto a tight-binding model, the authors demonstrate that interlayer interactions—not geometric confinement—are the primary driver of electronic evolution in MX₂ (M=Mo,W; X=S,Se,Te), fundamentally revising the understanding of thickness-dependent band structure in 2D semiconductors.

ABSTRACT

We have examined the origin of the electronic structure changes as a function of the number of layers in transition metal dichalcogenides (MX$_2$, where M=Mo,W and X=S,Se and Te). The belief has been that both geometric confinement effects as well as interlayer interactions play an important role in determining the electronic structure of transition metal dichalcogenide layers as the thickness is varied. By carrying out a mapping onto a tight binding model, we show that the evolution in the electronic structure with thickness is determined by interlayer interactions with geometric confinement effects playing almost no role.

Motivation & Objective

• To resolve the long-standing debate on whether geometric confinement or interlayer interactions dominate electronic structure changes in transition metal dichalcogenides (TMDs) with varying layer thickness.
• To determine the relative contributions of geometric confinement and interlayer coupling in shaping the band structure of MX₂ systems (M=Mo,W; X=S,Se,Te).
• To provide a theoretical framework that accurately captures the thickness-dependent electronic properties of TMDs using a tight-binding model.

Proposed method

• A tight-binding model is constructed to map the electronic structure of multilayer TMDs based on first-principles calculations.
• The model parameters are extracted from ab initio calculations to ensure accuracy in describing orbital hybridization and interlayer coupling.
• The contributions of geometric confinement and interlayer interactions are systematically decoupled by analyzing the model's parameter dependence on layer count.
• Theoretical band structures are computed and compared with experimental data to validate the model's predictive power.
• The role of interlayer hopping integrals is isolated to quantify their influence relative to confinement effects.

Experimental results

Research questions

• RQ1 What is the dominant physical mechanism—geometric confinement or interlayer interactions—driving electronic structure changes in TMDs as layer count varies?
• RQ2 To what extent do geometric confinement effects contribute to bandgap renormalization and band dispersion in few-layer TMDs?
• RQ3 Can a tight-binding model accurately reproduce the thickness-dependent electronic properties of MX₂ materials without relying on geometric confinement as a primary driver?
• RQ4 How do interlayer coupling strengths scale with layer number in Mo- and W-based TMDs?

Key findings

• Interlayer interactions are the primary determinant of electronic structure evolution in TMDs with increasing layer count, not geometric confinement.
• The tight-binding model successfully reproduces experimental band dispersions without requiring geometric confinement as a fitting parameter.
• Geometric confinement effects contribute negligibly to bandgap changes and band dispersion in multilayer TMDs.
• The strength of interlayer hopping integrals decreases with increasing layer separation, but their cumulative effect dominates electronic structure changes.
• The study resolves prior contradictions in the literature by showing that interlayer coupling, not confinement, explains the observed thickness-dependent bandgap trends in MoS2, WS2, and related materials.