GROUP THEORY SYMBOL

GTTbSpinOrbit

GTTbSpinOrbit[hamiltonian,spin-orbit interaction]
adds spin-orbit coupling to a given tight-binding Hamiltonian due to a specified spin-orbit interaction.

DetailsDetails

  • A Hamiltonian with spin-orbit coupling (SOC) is constructed in two steps. First, the Hamiltonian without SOC is needed, and second GTTbSpinOrbit can be used to add SOC.
  • The spin-orbit interaction is specified by a vector of the following form:
  • spin-orbit interaction = {atom1,atom2,...};
    atom1={bdim,l,pos,ξ}
  • The dimension of the block corresponding to atom1 in the Hamiltonian hamiltonian is given by bdim. The position of the block with angular momentum l for inclusion of SOC is determined by pos. ξ is the strength of SOC.
  • The Hamiltonian without SOC can be calculated using GTTbHamiltonian.
  • The following option canb e used:
  • GOVerboseFalseControls the output of additional information
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

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The Hamiltonian for the fcc structure is already constructed and will be read from file:

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We assume that the Hamiltonian for Au will be constructed. At first, the structure of the standard fcc-Hamiltoninan is shown.

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The fcc Hamiltonian will be doubled. It represents the up and down spin directions without SOC.

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The SOC will be introduced for the d electrons.

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The difference of the two Hamiltonians demonstrates, which matrix elements mediate the SOC.

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  • This can be compared with the structure of the matrices given by GTTbSpinMatrix .

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