(This example details the calculation from the Tutorial/Getting Started)
The TB-model for Graphene¶
The electronic structure of graphene is well described by a simple tight-binding model that only uses one \(p_z\) orbital in a hexagonal unit cell with two equivalent carbon atoms. These atoms are located on the different subbattices, A and B, and don't have an on-site energy term.
Though the model is relative simple, it is used suite often in the literature.
The code below illustrates the building of the
pb.lattice for graphene:
- define the parameter (\(t\) in \(eV\))
- define the vectors of the unit-cell (\(\vec a_1\) and \(\vec a_2\) in units of \(a\), length of the unit-cell)
- create a
- define the on-site energies
- define the hopping parameters
- 1 normal hopping within the unit cell
- 2 rotated hopping \(\pm 2 \pi/3\) to neighbouring cells
- return the
pb.lattice-object to be used by KITE
We can visualize this lattice using the following code:
We can make the
Now, run the KITEx program and the KITE-tools.