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

Abstract

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 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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Cited by in corpus (5)

• Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues
• Irreducibility of the Bloch Variety for Finite-Range Schrödinger Operators
• Topics on Fermi varieties of discrete periodic Schrödinger operators
• Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on ${\mathbb{Z}}^2$
• Spectra of Regular Quantum Trees: Rogue Eigenvalues and Dependence on Vertex Condition