GROUP THEORY SYMBOL

GTTbMatrixElement

GTTbMatrixElement[l1,m1,l2,m2,shell]
gives the decomposition of the tight-binding three-center integral between atom1 and atom2 , when atom2 belongs to the neighborhood shell and atom2 is located in direction relative to atom1.

DetailsDetails

  • In tight-binding theory the following integrals
  • have to be calculated. The Hamiltonian is represented in a Löwdin basis. labels the atomic site and the angular symmetry with respect to this site. The energy integrals are expressed as a linear combination of two-center integrals in dependence on the direction consines of the distance vector .
  • The following options can be given:
  • GOTbBasis0Supresses superscripts with element names
    GOTbRule1Selects substitution rules
  • See: A.V. Podolskiy, P. Vogl,Compact expression for the angular dependence of tight-binding Hamiltonian matrix elements, Phys. Rev. B 69, 233101 (2004)
  • W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.4

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package.

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The tight-binding matrix element will be expressed in terms of two-center-paramters and the direction cosines of the vector between the two atoms.

At the first atom a orbital is localized, at the second atom an orbital . The distance belongs to the nearest neighbor shell.

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Usually , and orbitals are used. The algorithm is general, also orbitals of higher angular momentum can be considered.

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In some considerations of semiconductors an excited orbital * is included in the basis. This can be simulated using .

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Options  (2)Options  (2)

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