GroupTheory`
GroupTheory`
GOTbOrthogonal
is an option of GTBandStructure used to define if orthogonal basis sets are assumed in the tight-binding calculations or not.
Details and Options
- If it is assumed that all basis functions at the lattice sites are orthogonal to each other the overlap matrix in the eigenvalue problem is the unity matrix. If a nonorthogonal basis is assumed, Hamiltonian matrix and overlap matrix have to be defined. A general eigenvalue problem has to be solved.
- Typical values for GOTbOrthogonal are:
-
True orthogonal basis sets are assumed False non-orthogonal basis sets are assumeds
Examples
Basic Examples (2)
The Hamiltonian will be prepared.
A list of k-points will be prepared.
In a non-orthogonal TB problem the Hamiltonian matrix and the overlap matrix define a general eigenvalue problem. As a simple example the orthogonal eigenvalue problem will be considered as a nonorthogonal one, providing a identity matrix as overlap matrix.
To show the structure of the matrices are plotted:
The results should be the same in a orthogonal and nonorthogonal scheme.
The same band structure appears, if the problem is considered orthogonal or non-orthogonal.
