Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the gyroid

DOI10.1016/j.aop.2012.08.001zbMath1254.81041arXiv1208.3262OpenAlexW2119333624MaRDI QIDQ714012

Ralph M. Kaufmann, Sergei Khlebnikov, Birgit Wehefritz-Kaufmann

Publication date: 19 October 2012

Published in: Annals of Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.3262

zbMATH Keywords

singularitiesdispersion relationswallowtailDirac pointsDouble Gyroidtorus cover

Mathematics Subject Classification ID

Selfadjoint operator theory in quantum theory, including spectral analysis (81Q10) Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices (81Q35) Quantum dots, waveguides, ratchets, etc. (81Q37) Quantum waveguides, quantum wires (82D77)

Related Items (7)

Chambers's formula for the graphene and the Hou model with kagome periodicity and applications ⋮ Re-gauging groupoid, symmetries and degeneracies for graph Hamiltonians and applications to the gyroid wire network ⋮ Local models and global constraints for degeneracies and band crossings ⋮ Bananas: multi-edge graphs and their Feynman integrals ⋮ Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the gyroid ⋮ Singular Geometry of the Momentum Space: From wire networks to quivers and monopoles ⋮ Theoretical Properties of Materials Formed as Wire Network Graphs from Triply Periodic CMC Surfaces, Especially the Gyroid

Cites Work

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• Singularities, swallowtails and Dirac points. An analysis for families of Hamiltonians and applications to wire networks, especially the gyroid
• Quantal phase factors accompanying adiabatic changes
• Morse Theory. (AM-51)
• The noncommutative geometry of the quantum Hall effect
• The Band Theory of Graphite

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