GTTbHamiltonianRS
GTTbHamiltonianRS[cluster,adjacency matrix,basis]
constructs a tight-binding Hamiltonian in real space.
Details and Options
- The tight-binding Hamiltonian in real space is calculated from the structural information stored in cluster and the neighborhood information given by the adjacency matrix.
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cluster Cluster as generated by means of GTCluster adjacency matrix Adjacency matrix as generated by GTAdjacencyMatrix basis List with information on the orbits to include, e. g. {{"Ti",1,{"d"}},{"O",3,{"p"}} This list corresponds to a model for BaTiO3 including the Ti and O atoms, but with a respricted basis set. - The following options can be given:
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GOTbBasis 0 Supresses supersripts with element names GOVerbose True Controls the output of additional information - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica
Examples
open allclose allBasic Examples (1)
We assume a simple cubic lattice.
The adjacency matrix is constructed now. Only nearest neighbors in the sc lattice are considered.
Now the Hamiltonian can be constructed. Only s orbitals are considered.
We assume some simple values for the parameters. Enter the values in numerical form to increase the calculation speed.
This choice of parameters leads to a DOS in the energy range [-6,6]. The calculation of the DOS takes some time!
An increase of the cluster size improves the result, but also increases the calculation time.
The numerical result can be compared with the analytic result.
Warnings due to convergence problems will be suppressed.
Comparison of the real space calculation and the analytical result.