GROUP THEORY SYMBOL

GOTbOrthogonal

GOTbOrthogonal
is an option of GTBandStructure used to define if orthogonal basis sets are assumed in the tight-binding calculations or not.

DetailsDetails

  • 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:
  • Trueorthogonal basis sets are assumed
    Falsenon-orthogonal basis sets are assumeds
  • This option is used by: GTBands ▫ GTBandStructure

ExamplesExamplesopen allclose all

Basic Examples  (2)Basic Examples  (2)

First load the package:

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The Hamiltonian will be prepared.

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A list of k-points will be prepared.

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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.

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To show the structure of the matrices are plotted:

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GTBands

The results should be the same in a orthogonal and nonorthogonal scheme.

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GTBandStructure

The same bandstructure appears, if the problem is considered orthogonal or non-orthogonal.

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