GroupTheory`
GroupTheory`

GTBandsPlotImprove

GTBandsPlotImprove[bands,text,modifications,minb,maxb]

is used to improve the labeling of bands with the notation of the irreducible representations stored in text in a plot. The bands from minb to maxb are analysed. With modifications the labeling can be modified.

Details and Options

  • GTBandsPlotImprove can be used to improve the labeling in plots resulting from the symmetry analysis of electronic or photonic band structures. Due to the degeneracy of the levels or small energetic distances of the eigenvalues the labels might be not placed in an optimal manner. This tool allows to shift or delete labels to create an optimal plot as a result of the symmetry analysis.
  • The list modifications allows the individual change of labels. It has the form: {{k-point, band, change}, {k-point, band, change},...}
  • change is either a relative shift of the y-coordinate of the label, or "D" to delete the label from the plot.
  • Alternatively Mathematica drawing tools can be used for an interactive change of the labels.
  • The following options can be given.
  • FrameLabel{" ", "a.u."}Axes labels
    GOLabelShift {0., 0.}shifts labels of Ireps
    JoinedTruecontinuous lines
    PlotLabel"Band structure"label of the plot
    PlotRangeAllset the range of the axes
    PlotStyle{{Thickness[Tiny], GrayLevel[0]}}styl of the plot
  • See: W. Hergert, M. Geilhufe, Group Theory in Solid State Physics and Photonics. Problem Solving with Mathematica, chapter 9.6.
  • J. D. Joannopoulos, S. G. Johnson, J. N. Winn, R. D. Meade, Photonic Crystals. Molding the flow of light, Princton 2008, p .70
  • MPB: http://ab-initio.mit.edu

Examples

open allclose all

Basic Examples  (1)

First load the package:

As an example an eigenmode calculated by means of MPB will be analysed. The data are stored in the subdirectory datasets.

A circular rod in a quadratic unit cell is considered. The radius of the rod is . The point group of the problem is .

It is checked, which objects are contained in the dataset.

The objects real and imaginary part (“z.r-new”, z.i-new”) of the mode after postprocessing with the tool mpb-data are necessary to prepare the mode for the symmetry analysis. It is possible to analyse only a certain range of the data.

The results of the symmetry analysis of bands 4 to 6 are stored in a list.

The output of the symmetry analysis can be used to improve the plot. All symmetry data are extracted from the third part of symm. The band structure has to be provided separately.

The modification list mod is used to correct the labels at Γ and the X point. The 6th label at the Γ point is deleted and the 4th label at the X point is shifted downwards. The row below the irreducible representation for each band contains the original energies (frequencies), i.e. y-coordinates. The next line contains the modified y-coordinates.

Options  (2)

FrameLabel, Joined, PlotLabel, PlotRange, and PlotStyle are options of Mathematica’s plot functions and not discussed here.

GOLabelShift  (1)

The standard offset for the labels here is {0,0}. All labels can be shifted together by means of GOLabelShift.

A large shift is used to demonstrate the effect. This general shift is not expressed in the second row of energy values in the table.