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.

References in corpus (8)

• The electronic properties of graphene
• Biased bilayer graphene: semiconductor with a gap tunable by electric field effect
• Asymmetry gap in the electronic band structure of bilayer graphene
• On the spectra of carbon nano-structures
• Landau level splittings, phase transitions, and non-uniform charge distribution in trilayer graphene
• Single-electron gap in the spectrum of twisted bilayer graphene
• Effective masses for zigzag nanotubes in magnetic fields
• Dirac cones for bi- and trilayer Bernal-stacked graphene in a quantum graph model

Cited by in corpus (6)

• 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
• Irreducibility of the Fermi Surface for Planar Periodic Graph 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