LCAO graphene orbitals wave functions

[jjakovac]

TL;DR

Application of the LCAO method to Graphene

Hello,
My name is Josip Jakovac, i am a student of the theoretical solid state physics phd studies.
First I want to apologize if my question has already been answered somewhere here, I googled around a lot, and found nothing similar.
My problem is that I need to apply TBA to Graphene. I went through the article that is attached below, got the 2nd quantization hamiltonian eigenvalues and eigenvectors, did taylor expansion around K and K', got Fermi velocity and K and K' points positions. But for further calculations I need wave functions of pi and pi* orbitals. Now, all the articles I found just mention the method of LCAO, and math besides it is generic. Can any of you explain to me how to go through the actual method for Graphene?

Another Idea is, as I used Quantum Espresso to do projections of wave functions over atomic orbitals, is it possible to extract orbital wave functions I need from there?

Thank you in advance,
Josip Jakovac

 

[DrDu]

An operator $a^\dagger_i$ generates a one particle state corresponding to a $p_z$ orbital centered at $R_i$, $p_z(r-R_i)=<r| a_i^\dagger|0>$. All one-particle state creation operators are linear superpositions of the $a^\dagger_i$, so it is easy to get a wavefunction.