An equivalence between monolayer and bilayer honeycomb lattices

Abstract

In this brief report, we show the equivalence between the tight-binding descriptions of the monolayer and bilayer honeycomb lattices. With appropriate value of the third nearest neighbors coupling, the Hamiltonian for a monolayer is equivalent to the low energy effective Hamiltonian for bilayer in the presence of trigonal warping. A simple physical argument is provided to explain this correspondance.

4 pages, 4 figures

References in corpus (7)

• The electronic properties of graphene
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Merging of Dirac points in a two-dimensional crystal
• Bloch-Zener oscillations across a merging transition of Dirac points
• Manipulation of Dirac points in graphene-like crystals
• Magnetic spectrum of trigonally warped bilayer graphene - semiclassical analysis, zero modes, and topological winding numbers
• Landau levels in deformed bilayer graphene at low magnetic fields

Cited by in corpus (14)

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• Tight-binding couplings in microwave artificial graphene
• Superradiant phase transition in electronic systems and emergent topological phases
• Orbital magnetism of coupled bands models
• Distant-Neighbor Hopping in Graphene and Haldane Models
• Manipulating type-I and type-II Dirac polaritons in cavity-embedded honeycomb metasurfaces
• Topological Route to New and Unusual Coulomb Spin Liquids
• Tunable orbital susceptibility in $\alpha$-${\mathcal{T}}_3$ tight-binding models
• Quantum topology identification with deep neural networks and quantum walks
• Neutral magic-angle bilayer graphene: Condon instability and chiral resonances
• Unprotected quadratic band crossing points and quantum anomalous Hall effect in FeB2 monolayer
• Quantifying the fragility of unprotected quadratic band crossing points
• Tight binding approximation for bilayer graphene and nanotube structures: from commensurability to incommensurability between the layers
• Dynamically Characterizing the Structures of Dirac Points via Wave Packets