GROUP THEORY SYMBOL

GTBandStructure

GTBandStructure[Hamiltonian,kpath,npoints,nband]
calculates and plots the band structure for a given Hamiltonian.

DetailsDetails

  • The Hamiltonian might be a tight-binding Hamiltonian, but also an electronic or photonics Hamiltonian based on plane-waves. The eigenvalue problem to calculate phonons can be provided too. The parameters in the Hamiltonians have to be substituted by numerical values. If the structure is indicated with kpath (for instance kpath="fcc"), the band structure will be calculated along a standard path in the Brillouin zone. On the other hand kpath might be a list containing the k-points and the labels of the points. npoints defines the number of points used along a line.
  • The tight-binding problems lead either to a simple eigenvalue problem or to a general eigenvalue problem. In case of the general eigenvalue problem Hamiltonian is a list containing two matrices, the Hamiltonian and the overlap matrix. The general case has to be indicated by the option GOTbOrthogonal.
  • The following options can be given:
  • FrameLabel{" ", "Energy"}
  • Option of ListPlot
    • GOFermiEnergy0Fermi energy
    GOIrepTextStyle{20,Darker[Red]}Defines style of label
    GOPhotonicFalseDistinguishes between the calculation of an electronic or a photonic bandstructure
    GOShift0Shifts the energies by a fixed value
    GOStore0Stores the data, if a file name is provided
    GOTbOrthogonalTrueOrthogonal basis sets are assumed.
    JoinedFalse
  • Option of ListPlot
    • LabelStyle{}
  • Option of ListPlot
    • PlotLabel"Band structure"
  • Option of ListPlot
    • PlotRangeAll
  • Option of ListPlot
    • PlotStyleBlue
  • Option of ListPlot
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.4.1, 9.5, 9.6.

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

In[1]:=
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Load the fcc Hamiltonian from file and prepare it for the calculation of the Cu band structure.

In[2]:=
Click for copyable input

Choose the path in Brillouin zone and calculate the band structure.

In[3]:=
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Out[3]=

Options  (7)Options  (7)

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