# LCAO graphene orbitals wave functions

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• jjakovac
In summary, Josip is a student of theoretical solid state physics and is looking for help applying TBA to Graphene. He has found some information but needs help understanding the method for Graphene. He also mentions the possibility of using Quantum Espresso for extracting the needed orbital wave functions.
jjakovac
TL;DR Summary
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?

Josip Jakovac

#### Attachments

• graphene_tight-binding_model-1ny95f1.pdf
1 MB · Views: 79
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.

## 1. What is LCAO graphene?

LCAO (Linear Combination of Atomic Orbitals) graphene is a theoretical model used to describe the electronic structure of graphene, a two-dimensional material consisting of a single layer of carbon atoms arranged in a hexagonal lattice.

## 2. What are orbitals in LCAO graphene?

Orbitals in LCAO graphene refer to the mathematical functions used to describe the probability of finding an electron in a specific energy state within the graphene lattice. These orbitals are derived from the combination of atomic orbitals of the individual carbon atoms in the lattice.

## 3. What is the significance of wave functions in LCAO graphene?

Wave functions in LCAO graphene represent the quantum mechanical description of the electron's behavior within the graphene lattice. They provide information about the electron's energy, position, and spin, and are essential for understanding the electronic properties of graphene.

## 4. How are the wave functions for LCAO graphene orbitals calculated?

The wave functions for LCAO graphene orbitals are calculated using a combination of quantum mechanics and mathematical techniques. This involves solving the Schrödinger equation for the graphene lattice and applying boundary conditions to determine the allowed energy states and corresponding wave functions.

## 5. What is the role of LCAO graphene orbitals wave functions in research?

LCAO graphene orbitals wave functions are crucial in research as they provide a theoretical framework for understanding the electronic properties of graphene. They are used in simulations and calculations to predict and analyze the behavior of electrons in graphene, which is essential for developing new applications and technologies based on this material.

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