Add Wannier interpolated bands (#1)

Co-authored-by: Michael F. Herbst <[email protected]>
mfherbst · May 22, 2023 · df25fbd · df25fbd
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diff --git a/3-wannierisation.jl b/3-wannierisation.jl
@@ -27,11 +27,13 @@ begin
 	using LazyArtifacts
 	using DFTK
 	using PlutoUI
+	using PlutoPlotly
 	using Plots
 	using SpecialFunctions
 	using Unitful
 	using UnitfulAtomic
 	using Wannier
+	import WannierPlots
 end
 
 # ╔═╡ b0e511c4-1fbc-42b5-9a25-030a28fe022f
@@ -118,10 +120,43 @@ wann_model = only(
 
 # ╔═╡ c5b2f3ac-02f8-4363-a925-32c132a1a0e2
 md"""
-!!! danger "TODO Visualisation"
-    Currently WannierPlots is still private ...
+Now let's use Wannier functions to interpolate band structures, and compare with DFTK bands.
+
+We first construct a `Wannier.InterpModel` specifically for Wannier interpolations. This lets us interpolate band structures using `Wannier.interpolate`, which returns a `Brillouin.KPathInterpolant` storing the kpoint coordinates on a kpath, and a matrix that contains eigenvalues.
+"""
+
+# ╔═╡ 29a426dd-34dd-4463-943d-1f01554cdc6e
+begin
+	interp_model = Wannier.InterpModel(wann_model)
+	kinter, bands_wann = Wannier.interpolate(interp_model)
+end
+
+# ╔═╡ aef8f91e-ff76-4420-8103-03b1a59f8403
+md"""
+The `Brillouin.KPathInterpolant` is also understood by DFTK, which we can leverage to compute the exact DFT band energies.
+"""
+
+# ╔═╡ 704fa624-ffd8-431b-a6cb-e2f41fce0e9b
+dftk_bands = DFTK.compute_bands(scfres.basis, kinter; scfres.ρ);
+
+# ╔═╡ a5250227-de3a-4f80-b114-45633107dbe5
+md"""
+Since DFTK uses atomic units, but `Wannier.interpolate` is hard-coded to electron volts, we also convert the DFTK data to `eV` and finally compare the two band structures.
 """
 
+# ╔═╡ e02c8fc7-fb01-460d-a3b8-23c2045f6666
+begin
+	to_eV(x)     = ustrip(auconvert(u"eV", x))
+	bands_dftk   = to_eV.(hcat(dftk_bands.λ...))
+	fermi_energy = to_eV(scfres.εF)
+end;
+
+# ╔═╡ d2ba1b6b-e51c-4779-8dae-c6e390f2adfa
+# wrap plot function so it works in Pluto notebook
+PlutoPlot(
+	WannierPlots.plot_band_diff(kinter, bands_dftk, bands_wann; fermi_energy).plot
+)
+
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 # ╠═b0e511c4-1fbc-42b5-9a25-030a28fe022f
@@ -132,3 +167,9 @@ md"""
 # ╠═89498877-ad4c-4d80-9661-54bf2ffafc4c
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 # ╟─c5b2f3ac-02f8-4363-a925-32c132a1a0e2
+# ╠═29a426dd-34dd-4463-943d-1f01554cdc6e
+# ╟─aef8f91e-ff76-4420-8103-03b1a59f8403
+# ╠═704fa624-ffd8-431b-a6cb-e2f41fce0e9b
+# ╟─a5250227-de3a-4f80-b114-45633107dbe5
+# ╠═e02c8fc7-fb01-460d-a3b8-23c2045f6666
+# ╠═d2ba1b6b-e51c-4779-8dae-c6e390f2adfa