GTAdjacencyMatrix
GTAdjacencyMatrix[cluster,neighbours]
constructs an adjacency matrix for cluster with the information about interactions to include stored in neighbors.
Details and Options
- cluster results from GTCluster. For the construction of real space tight-binding Hamiltionians it is necessary to construct an adjacency matrix. In the element
is stored, which atoms are at the sites 
and 
and to which neighbor shell with respect to the interaction of the two sorts they belong. - The information about the interactions is stored in neighbours. The list consists of two sublists. The first is an
square matrix containing at position (
,
) a list of shells to take into account for the interaction of the atoms 
,
. The second list is a list of names of atoms. - The following options can be given:
-
GOPlot False Plots the adjacency matrix GOSort False Defines a canonical order - See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.7.3
Examples
open allclose allBasic Examples (1)
The adjacency matrix of a cluster with fcc structure should be constructed. The corresponding structure file has to be loaded.
Choose the corresponding structure from the structure data file and modify it accordingly.
Calculate a cluster with fcc structure. The lattice constant ist set to a=1 and the distance from the origin is <1.5
We have to decide, which kind of neighbors should be included. If first and second neighbors will be included, the corresponding distances between the atoms in fcc structure are 1/
The necessary information for the construction of the adjacency matrix is:
This information can be visualized:
The adjacency matrix is constructed and stored in compact form:
