Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene

@article{Fisher2020ReducibleFS,
title={Reducible Fermi Surface for Multi-layer Quantum Graphs Including Stacked Graphene},
author={L. R. Fisher and Wei Li and Stephen P. Shipman},
journal={Communications in Mathematical Physics},
year={2020},
volume={385},
pages={1499 - 1534}
}
• Published 28 May 2020
• Mathematics, Physics
• Communications in Mathematical Physics
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…
16 Citations
• Mathematics
Letters in Mathematical Physics
• 2020
We prove that the Fermi surface of a connected doubly periodic self-adjoint discrete graph operator is irreducible at all but finitely many energies provided that the graph (1) can be drawn in the
• Physics, Mathematics
• 2021
We present full description of spectra for a Hamiltonian defined on periodic hexagonal elastic lattices. These continua are constructed out of Euler-Bernoulli beams, each governed by a scalar-valued
• Physics
• 2022
. In a tight-binding model of AA-stacked bilayer graphene, it is demonstrated that a bound defect state within the region of continuous spectrum can exist stably with respect to variations in the
. Let Γ = q 1 Z ⊕ q 2 Z ⊕· · ·⊕ q d Z , where q l ∈ Z + , l = 1 , 2 , · · · , d . Let ∆+ V be the discrete Schr¨odinger operator, where ∆ is the discrete Laplacian on Z d and the potential V : Z d →
• Wencai Liu
• Mathematics
Communications in Mathematical Physics
• 2022
. Let Γ = q 1 Z ⊕ q 2 Z with q 1 ∈ Z + and q 2 ∈ Z + . Let ∆+ X be the discrete periodic Schr¨odinger operator on Z 2 , where ∆ is the discrete Laplacian and X : Z 2 → C is Γ-periodic. In this paper,
• Wencai Liu
• Mathematics
Geometric and Functional Analysis
• 2022
Let $$H_0$$ H 0 be a discrete periodic Schrödinger operator on $$\ell ^2(\mathbb {Z}^d)$$ ℓ 2 ( Z d ) : \begin{aligned} H_0=-\Delta +V, \end{aligned} H 0 = - Δ + V , where $$\Delta$$ Δ is the
• Wencai Liu
• Mathematics
Journal of Mathematical Physics
• 2022
This is a survey of recent progress on the irreducibility of Fermi varieties, rigidity results and embedded eigenvalue problems of discrete periodic Schrödinger operators.
• Materials Science
Annales Henri Poincaré
• 2021
We investigate the spectrum of Schrödinger operators on finite regular metric trees through a relation to orthogonal polynomials that provides a graphical perspective. As the Robin vertex parameter

References

SHOWING 1-10 OF 65 REFERENCES

• S. Shipman
• Mathematics
Journal of Spectral Theory
• 2019
This work constructs a class of non-symmetric periodic Schrodinger operators on metric graphs (quantum graphs) whose Fermi, or Floquet, surface is reducible. The Floquet surface at an energy level is
• Physics
Journal of Physics A: Mathematical and Theoretical
• 2020
A quantum graph model for a single sheet of graphene is extended to bilayer and trilayer Bernal-stacked graphene; the spectra are characterized and the dispersion relations explicitly obtained; Dirac
• Physics
• 2021
Abstract We propose an extension, of a quantum graph model for a single sheet of graphene, to multilayer AA-stacked graphene and also to a model of the bulk graphite. Spectra and Dirac cones are
• Physics
• 2007
Abstract.We employ the tight binding model to describe the electronic band structure of bilayer graphene and we explain how the optical absorption coefficient of a bilayer is influenced by the
• Physics
• 2010
The electronic properties of graphene, a two-dimensional crystal of carbon atoms, are exceptionally novel. For instance, the low-energy quasiparticles in graphene behave as massless chiral Dirac
• Physics
• 2006
Within a tight-binding approach we investigate how the electronic structure evolves from a single graphene layer into bulk graphite by computing the band structure of one, two, and three layers of
• Physics
Physical review letters
• 2016
The results indicate the importance of a previously unaccounted band structure parameter which, together with a more accurate estimate of the other tight-binding parameters, results in a significantly improved determination of the electronic and Landau level structure of TLG.
• Physics
• 2004
The aim of this study is to explain how a quantum network can be used as simple model to calculate complex band structures. The paper contains an introduction, a mathematical exposure of the method,
• Mathematics
• 2006
We consider the magnetic Schr\"odinger operator on the so-called zigzag periodic metric graph (a quasi 1D continuous model of zigzag nanotubes) with a periodic potential. The magnetic field (with the
• Physics
Inventiones mathematicae
• 2019
We consider a quantum graph as a model of graphene in magnetic fields and give a complete analysis of the spectrum, for all constant fluxes. In particular, we show that if the reduced magnetic flux