Abstract
In this chapter, we describe the crystal and reciprocal lattices of bilayer graphene. We also discuss briefly the symmetry of the crystal lattice. We then introduce the tight-binding model for \(\pi \) electrons in bilayer graphene. We start with a general formulation valid for all points in the Brillouin zone and the resulting electronic structure. Next, we concentrate on the linear approximation of that model around the corners of the Brillouin zone.
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Notes
- 1.
We neglect in Eq. (2.6a) a factor of \(3\gamma _{n}\) appearing on the diagonal as it only leads to a shift of zero on the energy scale.
- 2.
For brevity, we omit the momentum index \(\varvec{p}\) and explicit dependence of the basis functions \(\phi _{\varvec{p},\xi ,i}\) on \(\varvec{r}\).
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Mucha-Kruczynski, M. (2013). The Tight-Binding Approach and the Resulting Electronic Structure. In: Theory of Bilayer Graphene Spectroscopy. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30936-6_2
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