Here you can find video tutorials to learn how to find Slater-Koster parameters via fitting to the data obtained from density functional theory (DFT). Step by step, you will find out how to generate a tight binding Hamiltonian.

We assume you have downloaded TBStudio and the Examples.

Two-Band Tight-Binding Hamiltonian for Graphene

To learn how to construct a TB model for graphene using Pz orbital by using TBStudio download this tutorial.

The unit cell of graphene’s lattice consists of two Carbon atoms and in this TB model, we introduce one Pz orbital for each of them. So we will have two bands for the whole system.

This TB hamiltonian is valid for the last valence and the first conduction bands. Starting from the 2-band TB model one can also find a low-energy effective Hamiltonian. we obtain the low-energy effective Model by first-order Taylor expansion about K point. The obtained Hamiltonian called Dirac low-energy Hamiltonian which is helpful for its electronic properties and behavior near the Dirac point.

2-Band TB Hamiltonian for Graphene (part 1)

In this video, you learn how to construct a first nearest neighbor TB model for Graphene, define the Pz orbitals for Carbon atoms and find the best fitting to the data obtained from DFT.

2-Band TB Hamiltonian for Graphene (part 2)

The following video shows how one can export the TB model as an explicit Hamiltonian. By using the code generator tools you can export the Hamiltonian in your desired programming languages.

Tight-Binding Hamiltonian for Gallenene-a100 (using s, px, py and pz orbitals)

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