GROUP THEORY SYMBOL

GTVibTbToPhononRule

GTVibTbToPhononRule[shells]
gives rules to transform a tight-binding p-Hamiltonian into a dynamical matrix.

DetailsDetails

  • The dynamical matrix to calculate phonon spectra for solids in a central force model can be generated starting from a tight-binding p-Hamiltonian.
  • The hopping parameters (ppπ) have to be set to zero. The elements (ppσ) have to be substituted by the spring constants and the masses. The command generates the substitution rules to transform the tight-binding Hamiltonian. The on-site elements in the dynamical matrix are not independent like in the tight-binding Hamiltonian, but have to be calculated in dependence on the spring constants and masses.
  • This is part of the transformation of the p-Hamiltonian to the dynamical matrix, but not part of the transformation rules.
  • The following option can be given:
  • GOTbBasis0Supresses superscripts with element names
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 13.2.2.
  • See for the idea: R.M. Martin, Electronic Structure - Basic Theory and Practical Methods, Cambridge University Press 2004, p. 404

ExamplesExamplesopen allclose all

Basic Examples  (1)Basic Examples  (1)

First load the package:

In[1]:=
Click for copyable input

The basis consists only of one atom. Superscripts to distinguish the different atoms in the basis are not necessary. Two shells are taken into account.

In[2]:=
Click for copyable input
Out[2]=

Options  (1)Options  (1)

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