GroupTheory`
GroupTheory`

GTTbHamiltonianOnsite

GTTbHamiltonianOnsite[hamiltonian, basis, structure] corrects the on-site elements for fcc, and bcc structure due to the crystal-field splitting

Details and Options

  • During automatic generation of two-center tight-binding Hamiltonians the crystal field splittings are not taken into account, i.e. for cubic structures only one on-site parameter (dd0) occurs for the d-level. GTTbHamiltonianOnsite allows to substitute (dd0) by two parameters (dd1) corresponding to t_(2g) orbitals and (dd2) corresponding to e_g orbitals.
  • Note, in the moment the module works only for Hamiltonians with spd-basis.
  • Parameter values for the one-site energies with crystal-field splitting are given in the "Handbook of the Band Structure of Elemental Solids". The split on-site parameters are provided in the database TB_Handbook. If the Hamiltonian is modified accordingly, the parametrization uses the correct parameters automatically.
  • The following options can be given:
  • GOVerbose FalseControls the output of additional information
  • D.A: Papaconstantopulos, Handbook of the Band Structure of Elemental Solids, Plenum Press, New York (2015)
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.4.

Examples

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Basic Examples  (1)

Load the Hamiltonian for for fcc structure with spd basis.

Create information about the basis.

The complete Hamiltonian can be listed by means of GTHamiltonianList

List the d-d block of the Hamiltonian

gonal matrix elements contain the on-site parameter (dd0). Now the splitting is introduced.

Options  (1)

GOVerbose  (1)

In the moment only minimal additional information appears.