Green’s Functions and DOS for Some 2D Lattices

Abstract

In this presentation 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 known, we hope that its derivation performed in a uniform way provides some pedagogical value.

Topological Atomic Chains on 2D Hybrid Structure

“…These functions are shown in Figure 2 (dashed black curves) and they correspond to the wide-band approximation, 2D rectangular lattice, and 2D honeycomb lattice, respectively. The surface DOS can be obtained exactly for different regular atomic latices [53][54][55][56] and their analytical forms are shown in the Appendix A. Note that such atomic lattices are fabricated in many experiments e.g., Pb atomic films form a hexagonal close-packed structure on Al(111) substrate, Sn atoms on Al(100) or Al(111) are found to form square-like structures [57,58] similarly, Sb films form square-like structures on Rh(111) [59].…”

“…where the summation over n concerns the energy bands in the Brillouin zone with the energy dispersion, ε n ( k). In 2D tight-binding models e.g., for square, triangle, honeycomb, graphene-like, Lieb, Kagome and other lattices the energy dispersion is derived analytically and can be expressed by means of the elliptic integrals [53][54][55][56]. In particular for 2D rectangular lattice one has:…”