2020/05/28 by Lee Fisher, Wei Li, Stephen P. Shipman
Chemistry · Materials Science · Mathematics · Physics and Astronomy · #Advanced Physical and Chemical Molecular Interactions #Algebraic number #Fermi Gamma-ray Space Telescope #Fermi energy #Fermi surface #Graphene research and applications #Polynomial #Quantum #Quantum graph #Spectral Theory in Mathematical Physics #Spectrum (functional analysis) #Surface (topology) #math-ph #math.MP #msc:47A75 #msc:47B25 #msc:47B40
paper · pdf · doi:10.1007/s00220-021-04120-z
arxiv created 2020/05/28 · openalex created_date 2020/06/05 · openalex publication_date 2021/06/29 · arxiv updated 2021/07/14 · openalex updated_date 2026/08/06
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.