GroupTheory`
GroupTheory`

GTPlotStateWeights

GTPlotStateWeights[cluster,distance,basis,wave function,scale]

demonstrates at which atoms of a cluster, the wave function (a solution of a real space tight-binding Hamiltonian) has the highest weights.

Details and Options

  • The real space tight-binding Hamiltionian of a cluster of ( - number of basis atoms, - number of atoms of -th sort in the cluster) atoms has the size ( - number of orbitals of -th sort). The Hamiltonian has therefore eigenvalues and the corresponding number of eigenvectors. The weight of the orbitals of an atom and sort is defined as:
  • ( - corresponding components in the eigenvector).
  • The wave function weights at the atoms are depicted by spheres of different size.
  • clustercluster of atoms, used to construct the Hamiltonian
    distanceminimal distance of atoms, used to construct bonds for the plot
    basisinformation about the basis used to construct the Hamiltonian
    wave functionan eigenvector of the Hamiltonian
    scalescaling factor, defines the radius of a sphere of maximal weight
  • The following options can be given:
  • GOColorScheme"ElementData"Defines the colors used to plot the atoms in the structure graph
    GOPlotTruePlots the graph
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica

Examples

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Basic Examples  (1)

For comparison the DOS is calculated in k-space

To demonstrate GTPlotStateWeights a small cluster is used.

The Hamiltonian in real space has the dimension 370x370. The corresponding cluster consists of 37 Ga and 37 As atoms. This real space Hamiltonian is also already prepared:

The cluster is also already calculated:

The density of states can be calculated.

Due to the small cluster size the real space DOS deviates from the k-space results. The comparison of both DOS calculations shows, that due to the surface of the cluster surface states appear in the band gap in the real space calculation.

GTFindStateNumbers can be used to find the numbers of eigenstates in an energy interval. To investigate the weights of the states on the different atoms, the eigenvectors have to be calculated too.

The plot demonstrates the state number 335, lying in the gap, is located on the surface of the cluster.

Options  (2)

ButtonBox["GOColorScheme", BaseStyle -> "Link", ButtonData -> "paclet:GroupTheory/ref/GOColorScheme"]  (1)

In the standard setting the colors are taken from "ElementData". The colors can be chosen explicitly.

ButtonBox["GOPlot", BaseStyle -> "Link", ButtonData -> "paclet:GroupTheory/ref/GOPlot"]  (1)

Suppress graphics output and get a graphics object.