Irreducibility of the Fermi surface for planar periodic graph operators

DOI10.1007/s11005-020-01311-yzbMath1502.39010arXiv1909.04197OpenAlexW3043451540MaRDI QIDQ2198358

Stephen P. Shipman, Wei Li

Publication date: 10 September 2020

Published in: Letters in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.04197

zbMATH Keywords

Fermi surfaceplanar graphgraph operatorgraph LaplacianFloquet surfacereducible algebraic variety

Mathematics Subject Classification ID

Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Discrete version of topics in analysis (39A12) Difference operators (39A70) Relationships between algebraic curves and physics (14H81) Partial difference equations (39A14)

Related Items (9)

Irreducibility of the Fermi variety for discrete periodic Schrödinger operators and embedded eigenvalues ⋮ Topics on Fermi varieties of discrete periodic Schrödinger operators ⋮ Irreducibility of the Bloch variety for finite-range Schrödinger operators ⋮ Flat bands of periodic graphs ⋮ Stable defect states in the continuous spectrum of bilayer graphene with magnetic field ⋮ Fermi isospectrality for discrete periodic Schrödinger operators ⋮ Algebraic properties of the Fermi variety for periodic graph operators ⋮ Fermi isospectrality of discrete periodic Schrödinger operators with separable potentials on \(\mathbb{Z}^2\) ⋮ Reducible Fermi surface for multi-layer quantum graphs including stacked graphene

Cites Work

• Eigenfunctions of unbounded support for embedded eigenvalues of locally perturbed periodic graph operators
• Magnetic Schrödinger operators on periodic discrete graphs
• On the structure of eigenfunctions corresponding to embedded eigenvalues of locally perturbed periodic graph operators
• Fluxes, Laplacians, and Kasteleyn's theorem
• Reducible Fermi surfaces for non-symmetric bilayer quantum-graph operators
• A toroidal compactification of the Fermi surface for the discrete Schrödinger operator
• On absence of embedded eigenvalues for schrÖdinger operators with perturbed periodic potentials
• Single Band Motion of Conduction Electrons in a Uniform Magnetic Field
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