GROUP THEORY SYMBOL

GTPwEmptyLatticeIrep

GTPwEmptyLatticeIrep[point group,reciprocal basis, k-point, gcut,number of bands]
determines the irreducible representations of the empty lattice band structure to a structure with point group. The reciprocal basis and the maximum length gcut of the reciprocal lattice vectors have to be provided. The analysis is done at a certain k-point, for a restricted number of bands.

DetailsDetails

  • GTPwHamiltonian allows to construct an empty lattice Hamiltonian, which can be used in GTBandStructure to plot the corresponding bands. GTPwEmptyLatticeIrep allows to determine the irreducible representations corresponding to the energy eigenvalues.
  • In this simple case no real wave function information is necessary, because due to the missing interaction the Hamiltonian is diagonal. From all reciprocal lattice vectors leading to the same energy a faithful representation is constructed and than reduced.
  • The following options can be given:
  • GOIrepNotation"Mulliken"Controls the notation of irreducible representation
    GOVerboseFalseControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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Pseudopotential parameters are not necessary to calculate an empty lattice band structure. Choose the corresponding structure from the structure data file and modify it accordingly. A fcc structure will be considered, i.e. the information for cu is fine.

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The Hamiltonian will be built for the empty lettice test.

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Choose the k path in accordance with the structure, i.e. here “fcc”:

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Calculate and plot the band structure:

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The point group for the cubic fcc structure is Oh.

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Calculate the reciprocal lattice vectors (units 2π/a) for the fcc lattice.

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Options  (2)Options  (2)

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