Abstract
In this chapter, we take advantage of the significant anisotropy of the 2D materials and InSe, which feature strong covalent bonding within crystalline layers, whilst the bonding between the layers has a comparatively weak van der Waals character. Each layer is reduced to a basis of its monolayer \(\mathbf {k\cdot p}\) bands, then in multilayer films we couple successive layers with tight-binding hops—which are between monolayer band states rather than atomic orbitals. A model developed using this approach is here described as a hybrid \(\mathbf {k\cdot p}\) tight-binding (HkpTB) model.
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Notes
- 1.
The parameter \(\nu \), which takes account of the extension of the wavefunction beyond the crystal sufrace, is reduced slightly in the fit to \(\nu =1.01\).
- 2.
Especially so since any symmetry breaking will come from the interband hops, as we explore in Chap. 4—therefore, when we correct the gap the effect will be even smaller.
- 3.
A significant contribution to the analysis in this section was made by A. Ceferino.
- 4.
\(E_zd_z\) due to a plane of charge with \(n_e=5\times 10^{12}\)Â cm\(^{-2}\) in vacuum would have an energy \({\sim }75\)Â meV, which can be neglected when considering subband energetics, given the scale of the gap between the monolayer states of 2.8Â eV.
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Magorrian, S.J. (2019). Hybrid \(\mathbf {k\cdot p}\) Tight-Binding Theory. In: Theory of Electronic and Optical Properties of Atomically Thin Films of Indium Selenide. Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-030-25715-6_3
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