Dirac cones for point scatterers on a honeycomb lattice (Q2802692)
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scientific article; zbMATH DE number 6574177
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Dirac cones for point scatterers on a honeycomb lattice |
scientific article; zbMATH DE number 6574177 |
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27 April 2016
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honeycomb lattice
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triangular lattice
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point scatterer
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Dirac point
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delta potential
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graphene
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Dirac cones for point scatterers on a honeycomb lattice (English)
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The purpose of this paper is to study the spectral properties of the Schrödinger operator with point scatterers on a triangular lattice and a honeycomb lattice. The areas of the fundamental domains are computed and shown on graphs. The eigenvalues and the spectrum of the periodic point scatterer are likewise computed and shown on graphs. Furthermore, graphs for front views of the first five dispersion bands are shown. Formulas and inequalities for the eigenvalues of the unperturbed operator \(\Delta(k)\) are proved. The local behaviour of dispersion bands near Dirac points is investigated. The proofs use Laurent expansion, Poisson summation formula and projection operators.
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