Green's functions and DOS for some 2D lattices

TL;DR

This paper provides a uniform derivation of Green's functions and density of states for common 2D lattices, serving as a pedagogical resource despite well-known results.

Contribution

It offers a consistent derivation of Green's functions and DOS for several 2D lattices, enhancing understanding and teaching.

Findings

Green's functions derived for square, triangular, honeycomb, kagome, and Lieb lattices

Density of states calculated for each lattice type

Results presented in a uniform, pedagogical manner

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.