GROUP THEORY SYMBOL

GTTbHamiltonianRS

GTTbHamiltonianRS[cluster,adjacency matrix,basis]
constructs a tight-binding Hamiltonian in real space.

DetailsDetails

  • The tight-binding Hamiltionian in real space is calculated from the structural information stored in cluster and the neighborhood information given by the adjacency matrix.
  • clusterCluster as generated by means of GTCluster
    adjacency matrixAdjacency matrix as generated by GTAdjacencyMatrix
    basisList with information on the orbits to include, e. g. {{"Ti",1,{"d"}},{"O",3,{"p"}} This list corresponds to a model for BaTiO3 including the Ti and O atoms, but with a respricted basis set.
  • The following options can be given:
  • GOTbBasis 0Supresses supersripts with element names
    GOVerboseTrueControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package.

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We assume a simple cubic lattice.

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A cluster is constructed.

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The adjacency matrix is constructed now. Only nearest neighbors in the sc lattice are considered.

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Now the Hamiltonian can be constructed. Only s orbitals are considered.

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We assume some simple values for the parameters. Enter the values in numerical form to increase the calculation speed.

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This choice of parameters leads to a DOS in the energy range [-6,6]. The calculation of the DOS takes some time!

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An increase of the cluster size improves the result, but also increases the calculation time.

The numerical result can be compared with the analytic result.

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Warnings due to convergence problems will be suppressed.

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Comparison of the real space calculation and the analytical resullt.

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