Green's functions and DOS for some 2D lattices

Abstract

In this note we present the Green's functions and density of states for the most frequently encountered 2D lattices: square, triangular, honeycomb, kagome, and Lieb lattice. Though the results are well know, we hope that their derivation performed in a uniform way is of some pedagogical value.

arXiv commentLatex, 6 pages, 5 eps files. As accepted for publication in Graphene

References in corpus (11)

• The electronic properties of graphene
• Application of the lattice Green's function for calculating the resistance of an infinite networks of resistors
• RKKY Interaction in Graphene from Lattice Green's Function
• Lattice dependence of saturated ferromagnetism in the Hubbard model
• Ruderman-Kittel-Kasuya-Yosida interaction in biased bilayer graphene
• Effect of magnetic field and chemical potential on the RKKY interaction in the $\alpha$-${\mathcal{T}}_3$ lattice
• Magnetoplasmons for the $\alpha$-T${}_3$ model with filled Landau levels
• Analytical results for Green's functions of lattice fermions
• On the density of states of graphene in the nearest-neighbor approximation
• Lattice Green's functions for kagome, diced and hyperkagome lattices
• RKKY plateau in zero- and one-dimensional triangular Kagome lattice models

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• Non-Hermitian catalysis of spontaneous symmetry breaking on Euclidean and hyperbolic lattices
• Particle-Hole Asymmetry and Pinball Liquid in a Triangular-Lattice Extended Hubbard Model within Mean-Field Approximation
• Superlinear Hall angle and carrier mobility from non-Boltzmann magnetotransport in the spatially disordered Yukawa-Sachdev-Ye-Kitaev model on a square lattice
• Walking on Archimedean Lattices: Insights from Bloch Band Theory
• Single impurity-induced localization transitions in electronic systems
• Impact of clustering of substitutional impurities on quasiparticle lifetimes and localization
• Discrete holography and density of states in the crossover from hyperbolic to Euclidean lattices
• Analytic density of states of two-dimensional Chern insulator
• Evolution of the Andreev bands in the half-filled superconducting periodic Anderson model