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arXiv · 2005.13764

Reducible Fermi surface for multi-layer quantum graphs including stacked graphene

Lee Fisher·Wei Li·Stephen P. Shipman
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Abstract

We construct two types of multi-layer quantum graphs (Schr\"odinger operators on metric graphs) for which the dispersion function of wave vector and energy is proved to be a polynomial in the dispersion function of the single layer. This leads to the reducibility of the algebraic Fermi surface, at any energy, into several components. Each component contributes a set of bands to the spectrum of the graph operator. When the layers are graphene, AA-, AB-, and ABC-stacking are allowed within the same multi-layer structure. Conical singularities (Dirac cones) characteristic of single-layer graphene break when multiple layers are coupled, except for special AA-stacking. One of the tools we introduce is a surgery-type calculus for obtaining the dispersion function for a periodic quantum graph by gluing two graphs together.

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Lee Fisher, Wei Li, Stephen P. Shipman. 2020-05-28. Reducible Fermi surface for multi-layer quantum graphs including stacked graphene. https://doi.org/10.1007/s00220-021-04120-z

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