pythonize and recolor NFEM

src/11_nearly_free_electron_model.md

 ```python tags=["initialize"]
+import matplotlib
+from matplotlib import pyplot
+
 import numpy as np
-import plotly.offline as py
-import plotly.graph_objs as go
+
+from common import draw_classic_axes, configure_plotting
+
+configure_plotting()
 
 pi = np.pi
 ```
@@ -50,7 +55,39 @@ In the free electron model, the dispersion is $E = \hbar^2 |\mathbf{k}|^2/2m$. T
 
 Within the **nearly free electron model** we start from the dispersion relation of free electrons and analyze the effect of introducing a weak lattice potential. The logic is very similar to getting optical and acoustic phonon branches by changing atom masses (and thereby reducing the size of the Brillouin zone). The lattice potential results in a band structure that is periodic in $k$-space, with a period given by the period of the reciprocal lattice:
 
-![](figures/nearly_free_electron_bands.svg)
+```python
+# Use colors from the default color cycle
+default_colors = pyplot.rcParams['axes.prop_cycle'].by_key()['color']
+blue, orange, *_ = default_colors
+
+def energy(k, V=1):
+    k = (k + pi) % (2*pi) - pi
+    k_vals = k + 2*pi * np.arange(-1, 2)
+    h = np.diag(k_vals**2) + V * (1 - np.identity(3))
+    return np.linalg.eigvalsh(h)
+
+energy = np.vectorize(energy, signature="(),()->(m)")
+
+fig, ax = pyplot.subplots(1, 1)
+
+momenta = np.linspace(-3*pi, 3*pi, 400)
+energies = energy(momenta, 0)
+max_en = 60
+energies[energies > max_en] = np.nan
+ax.plot(momenta, energies, c=blue)
+energies = energy(momenta, 3)
+max_en = 60
+energies[energies > max_en] = np.nan
+ax.plot(momenta, energies, c=orange)
+
+ax.set_xlabel("$ka$")
+ax.set_ylabel("$E$")
+ax.set_ylim(-.5, max_en + 5)
+ax.set_xticks(pi * np.arange(-3, 4))
+ax.set_xticklabels(fr"${i}\pi$".replace("1", "") if i else "$0$" for i in range(-3, 4))
+
+draw_classic_axes(ax, xlabeloffset=4)
+```
 
 In this figure, the red curves represent the nearly-free electron dispersion, which differs from the free-electron dispersion (black curves) because of the interaction with the lattice. We see that **band gaps** open where two copies of the free-electron dispersion cross. A key goal of this lecture is to understand how the weak interaction with the lattice leads to this modified band structure.
 
@@ -165,21 +202,65 @@ There are several common ways to **plot** the same dispersion relation (no diffe
 
 Repeated BZ (all possible Bloch bands):
 
-![](figures/nearly_free_electron_bands.svg)
+```python
+fig
+```
 
 * Contains redundant information
 * May be easier to count/follow the bands
 
 Reduced BZ (all bands within 1st BZ):
 
-![](figures/reduced_nearly_free_electron_bands.svg)
+```python
+fig, ax = pyplot.subplots(1, 1)
+
+momenta = np.linspace(-pi, pi, 400)
+energies = energy(momenta, 0)
+max_en = 60
+energies[energies > max_en] = np.nan
+ax.plot(momenta, energies, c=blue)
+energies = energy(momenta, 3)
+max_en = 60
+energies[energies > max_en] = np.nan
+ax.plot(momenta, energies, c=orange)
+
+ax.set_xlabel("$ka$")
+ax.set_ylabel("$E$")
+ax.set_ylim(-.5, max_en + 5)
+ax.set_xticks(pi * np.arange(-1, 2))
+ax.set_xticklabels(r"$-\pi$ $0$ $\pi$".split())
+
+draw_classic_axes(ax, xlabeloffset=4)
+```
 
 * No redundant information
 * Hard to relate to original dispersion
 
 Extended BZ (n-th band within n-th BZ):
 
-![](figures/extended_nearly_free_electron_bands.svg)
+```python
+fig, ax = pyplot.subplots(1, 1)
+
+momenta = np.linspace(-3*pi, 3*pi, 400)
+energies = energy(momenta, 0)
+max_en = 60
+energies[energies > max_en] = np.nan
+energies[~((abs(momenta) // pi).reshape(-1, 1) == np.arange(3).reshape(1, -1))] = np.nan
+ax.plot(momenta, energies, c=blue)
+energies = energy(momenta, 3)
+max_en = 60
+energies[energies > max_en] = np.nan
+energies[~((abs(momenta) // pi).reshape(-1, 1) == np.arange(3).reshape(1, -1))] = np.nan
+ax.plot(momenta, energies, c=orange)
+
+ax.set_xlabel("$ka$")
+ax.set_ylabel("$E$")
+ax.set_ylim(-.5, max_en + 5)
+ax.set_xticks(pi * np.arange(-3, 4))
+ax.set_xticklabels(fr"${i}\pi$".replace("1", "") if i else "$0$" for i in range(-3, 4))
+
+draw_classic_axes(ax, xlabeloffset=4)
+```
 
 * No redundant information
 * Easy to relate to free electron model