Paper Details

Name: Pooja Kumari
Country: India

Year: 2025
Volume: Volume-12, Issue-2 (July-December)
Page Number: 296-303
DOI: https://doi.org/10.5281/zenodo.17814763

ABSTRACT
Van der Waals (vdW) solids, comprising layered two-dimensional (2D) materials such as
graphene, hexagonal boron nitride (h-BN), transition-metal dichalcogenides (TMDs), and
artificially stacked heterostructures, have emerged as a transformative class of quantum
materials where electronic dispersion can be tuned through stacking, twist angles, external
fields, and strain. The ability to modulate band curvature, Fermi velocity, effective mass, and
bandgap via interlayer coupling has opened promising avenues in nanoelectronics,
valleytronics, and optoelectronics. This paper presents an analytical study of electronic
dispersion engineering in vdW solids through continuum band modelling, tight-binding
approximations, and perturbative analysis of interlayer interactions. The study identifies how
weak vdW interlayer coupling preserves individual layer symmetry while enabling tunable
hybridisation near high-symmetry points such as K, K′, M, and Γ. Analytical derivations
highlight how interlayer distance and twist angle modify the overlap integral and hopping
parameters, leading to reconstructed mini-bands, flatband formation, and moiré-induced
dispersion renormalisation. Graphene bilayers illustrate how small twist angles (<2°) reduce
Fermi velocity and yield flatbands associated with strong correlation, while similar
engineering in MoS₂, WS₂, and MoSe₂ demonstrates tunable direct–indirect band transitions
under vertical fields and interlayer shear. The study further examines dispersion anisotropy in
black phosphorus, where effective mass variation along armchair and zigzag directions can
be analytically captured via k·p theory. In all these systems, the analytical models align with
experimentally observed electro-absorption spectra, ARPES measurements, and magnetotransport signatures.
Keywords: Van der Waals solids; electronic dispersion engineering; moiré superlattices;
twisted bilayer graphene; transition-metal dichalcogenides (TMDs); black phosphorus; tightbinding model; k·p perturbation theory.