Green Functions of Graphene: An Analytic Approach

TL;DR

This paper derives and simplifies the lattice Green Functions for graphene using an extended tight-binding model, revealing significant differences from simpler models and providing a practical computational approach.

Contribution

It introduces an analytic method for calculating graphene's Green Functions with extended hopping and overlap, improving accuracy over traditional models.

Findings

Extended model alters electronic structure significantly

Single integral approximation for GFs is highly accurate

Provides a computational blueprint for advanced electronic analysis

Abstract

In this article we derive the lattice Green Functions (GFs) of graphene using a Tight Binding Hamiltonian incorporating both first and second nearest neighbour hoppings and allowing for a non-orthogonal electron wavefunction overlap. It is shown how the resulting GFs can be simplified from a double to a single integral form to aid computation, and that when considering off-diagonal GFs in the high symmetry directions of the lattice this single integral can be approximated very accurately by an algebraic expression. By comparing our results to the conventional first nearest neighbour model commonly found in literature, it is apparent that the extended model leads to a sizeable change in the electronic structure away from the linear regime. As such, this article serves as a blueprint for researchers who wish to examine quantities where these considerations are importa