Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene

  title={Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene},
  author={L. R. Fisher and Wei Li and Stephen P. Shipman},
  journal={Communications in Mathematical Physics},
  pages={1499 - 1534}
We construct two types of multi-layer quantum graphs (Schrödinger 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… 

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