Projected Band Structure

Here, we will show how to plot projected band structure from PROCAR, as the first example.

To finish this task, we need three packages.

using MatterEnv
using Plots
using LaTeXStrings

The first step is to load metadata from PROCAR file, you can check the details from this section. Here, we use a GGA+U+SOC result with lorbit=12 tag.

projection_all, _, _, projection_z, kpoints, bands = load_procar("PROCAR"; noncollinear=true)

To make the image look better, we set Fermi energy to be 0.

fermi_energy =  -3.0009
shift_energy!(bands, -fermi_energy)

Then we define two transformation matrix to do orbit transformation. You chan check the details from this section

transformation_matrix1 =
[
    -1/√3   √2/√3   0       0       0;
    √2/√3   1/√3    0       0       0;
    0       0       1       0       0;
    0       0       0       √2/√3   1/√3;
    0       0       0       -1/√3   √2/√3;
]
transformation_matrix2 =
[
    1       0       0       0       0;
    0       1/√2    0       0       1/√2im;
    0       0       1       0       0;
    0       0       0       1       0;
    0       1/√2    0       0       -1/√2im;
]
projection_transformation!(projection_all, transformation_matrix1, transformation_matrix2)

Since VASP doesn't distinguish between major spin and minor spin, we use a trick.

projection, bands = distinguish_spin(projection_all, projection_z, bands)

Finally, we can plot the projected band structure.

critical_points = ["Γ", "M", "K", "Γ"]      # Critical points of chosen k points
tolerance = 0.15                            # minimum value of projection character value to be plotted
magnify = 7.0                               # marker_size = magnify * projection_character
max_size = 3.0                              # maximum value of marker size

# some basic setting for the figure
plot(
    dpi = 300,
    size = (800, 600),
    framestyle = :box,
    fontfamily = "Times Roman",
    ylabel = "Energy (eV)",
    guidefontsize = 25,
    ylim = (-3.0, 7.0),
    legend = false,
    grid = :x,
    gridstyle = :dash,
    gridalpha = 1,
    tick_direction = :in,
    yticks = -2:2:6,
    yminorticks = false,
    tickfontsize = 23,
    bottom_margin = 1.0Plots.cm,
    left_margin = 1.0Plots.cm,
)

# plot all bands. black solid for spin up and gray dash line for spin down
plot!(bands, kpoints; critical_points = critical_points, colorlist = [:black, :black], stylelist = [:solid, :dash])

# plot projected band structure
plot!(projection, kpoints, bands; ion=1, orbit=7, markeralpha =1, markerstrokecolor=:red, markercolor=:red,  tolerance=tolerance, max_size=max_size, magnify=magnify)
plot!(projection, kpoints, bands; ion=1, orbit=6, markeralpha =1, markerstrokecolor=:orange, markercolor=:orange, tolerance=tolerance, max_size=max_size, magnify=magnify)
plot!(projection, kpoints, bands; ion=1, orbit=9, markeralpha =1, markerstrokecolor=:blue, markercolor=:blue, tolerance=tolerance, max_size=max_size, magnify=magnify)
plot!(projection, kpoints, bands; ion=1, orbit=5, markeralpha =1, markerstrokecolor=:green, markercolor=:green, tolerance=tolerance, max_size=max_size, magnify=magnify)
plot!(projection, kpoints, bands; ion=1, orbit=8, markeralpha =1, markerstrokecolor=:green, markercolor=:green, tolerance=tolerance, max_size=max_size, magnify=magnify)

# grid line
plot!([0, length(kpoints)], [0, 0], linecolor = :gray, linestyle = :dash, label=nothing)

savefig("band.png")

You can download this example script from here.