GroupTheory`

GTTbRealSpaceMatrix

GTTbRealSpaceMatrix[atom1,atom2,shell]

constructs the interaction of atom1 and atom2 in a tight-binding Hamiltonian in a certain neighbor shell.

Details and Options

GTTbRealSpaceMatrix calculates the interaction of two atoms in the tight-binding formalism in two-center form, i.e. the matrix is expressed in two-center parameters and the direction cosines DL, DM, DN of the distance vector.
shell is the number of the neighbor shell (shell = 1,2,...).
The atoms are described by lists
atom= {chemical symbol,{angular momenta}}
As an example:
atom1 = {"Ga",{"s,","p","s*"}}
The following option can be given:
GOTbBasis 0 Supresses superscripts with element names
See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica

Examples

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Basic Examples (1)

First load the package:

Both atoms are of the same sort. A restricted basis set of s and p wave functions will be used.

The interaction will describe a nearest neighbor interaction.

Options (1)

GOTbBasis (1)

If different types of atoms appear, we have to distinguish the tight-binding parameters accordingly. GaAs will be described by a basis set of s,p,s* orbitals for Ga and As.

We construct the interaction of Ga and As for the next nearest neighbor interaction.

The nearest neighbor interaction of Ga atoms is given by:

GOTbBasis has to be different from 0 to construct superscripts containing the interacting atoms. The information about the interacting atoms is taken from atom1 and atoms2 and not from the value of GOTbBasis.