GTDensityOfStatesRS
GTDensityOfStatesRS[Hamiltonian, parameters] is used to calculate the density of states of a Hamiltonian in real space.
Details and Options
- For a real space NxN Hamiltonian matrix, the density of states is computed by a sum of Gaussians (width σ) located at the N eigenvalues.
- Alternatively, a list of N eigenvalues can be provided. This becomes relevant, e.g., when using external libraries to diagonalize a Hamiltonian. For example, a Hamiltonian can be constructed using GTTbHamiltonianRS and exported to FORTRAN using GTTbRSToFortran. Then, the eigenvalues can be calculated using numerical libraries.
- The vector parameters contains the following quantities:
- parameters = {nbas, nat, emin, emax, ne, σ, scale}
-
nbas number of atoms in the basis nat number of atoms in the cluster [emin,emax] energy intervall for calculation of density of states ne number of energy points used to calculate the density of states σ width of the Gaussians (if σ = 0 the energy step width is used) scale The DOS can be scaled by the factor scale. This is sometimes helpful for comparisons. - The following options can be given:
-
GOStore 0 is an option which controls the output of data to files. PlotRange All is an option for graphics functions that specifies what range of coordinates to include in a plot. FrameLabel {Energy, DOS} is an option for Graphics, Manipulate, and related functions that specifies labels to be placed on the edges of a frame. GOFermiEnergy -100000 is an option to decide if the Fermi energy is calculated after the calculation of the denstiy of states (DOS). PlotLabel "Density of States" is an option for graphics functions that specifies an overall label for a plot. PlotStyle RGBColor[1, 0, 0] is an option for plotting and related functions that specifies styles in which objects are to be drawn. GOPlotDos "DOS" is an option to decide if the density of states, the integrated density of states or partial densities of states, or all will be presented. - 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 (2)
GaAs - real space vs k-space (1)
The k-space Hamiltonian is loaded from a file. It was constructed using a 
The density of states in k-space:
The real-space Hamiltonian has the dimension 7090x7090 and is constructed from a cluster of 709 Ga and 709 As atoms.
The comparison of both DOS calculations shows, that surface states appear in the band gap in the real space calculation.
DOS from a list of eigenvalues (1)
Options (4)
FrameLabel, PlotLabel, PlotRange, and PlotStyle are Mathematica options used in GTDensityOfStatesRS and will be not discussed here.
