Update 4_sommerfeld_model.md

src/4_sommerfeld_model.md

@@ -37,7 +37,7 @@ $$
 kf = 3;
 extrapol = 1.1;
 ks = np.arange(-kf, kf+1);
-kcont = np.linspace(-extrapol*kf, extrapol*kf, 1000);
+kcont = np.linspace(-extrapol*kf, extrapol*kf, 200);
 
 Edis = ks**2;
 Econt = kcont**2;
@@ -45,13 +45,13 @@ Econt = kcont**2;
 fig = pyplot.figure();
 ax = fig.add_subplot(111);
 ax.plot(kcont, Econt, 'b-');
-ax.plot(ks, Edis, 'k.');
+ax.plot(ks, Edis, 'k.', markersize=10);
 for i in range(2*kf + 1):
     ax.plot([ks[i], ks[i]], [0.0, Edis[i]], 'k:');
 ax.set_xlim(-3.75, 3.75);
 ax.set_ylim(0.0, 11);
 
-ax.set_xlabel(r"$k \quad \left[ \frac{2 \pi}{L} \right]$");
+ax.set_xlabel(r"$k \enspace \left[ \frac{2 \pi}{L} \right]$");
 ax.set_ylabel(r"$\varepsilon$");
 
 ax.set_xticklabels([""] + ks.tolist() + [""]);
@@ -122,7 +122,34 @@ For copper, the Fermi energy is ~7 eV. It would take a temperature of $\sim 70 0
 
 The total number of electrons can be expressed as $N=\frac{2}{3}\varepsilon_{\rm F}g(\varepsilon_{\rm F})$.
 
-![](figures/fermi_level.svg)
+```python
+kf = 3.0;
+extrapol = 4.0/3.0;
+kfilled = np.linspace(-kf, kf, 500);
+kstates = np.linspace(-extrapol*kf, extrapol*kf, 500);
+
+Efilled = kfilled**2;
+Estates = kstates**2;
+
+fig = pyplot.figure();
+ax = fig.add_subplot(111);
+ax.plot([kf, kf], [0.0, kf*kf], 'k:');
+ax.plot(kstates, Estates, 'k--');
+ax.plot(kfilled, Efilled, 'b-', linewidth=4);
+ax.axhline(kf*kf, linestyle="dotted", color='k');
+
+ax.set_xticks([kf]);
+ax.set_yticks([kf*kf]);
+ax.set_xticklabels([r"$k_F$"]);
+ax.set_yticklabels([r"$\varepsilon_F$"]);
+
+ax.set_xlabel(r"$k$");
+ax.set_ylabel(r"$\varepsilon$");
+
+ax.set_xlim(-kf*extrapol, kf*extrapol);
+ax.set_ylim(0.0, kf*kf*extrapol);
+draw_classic_axes(ax);
+```
 
 The bold line represents all filled states at $T=0$. This is called the _Fermi sea_. Conduction takes place only at the _Fermi surface_: everything below $\varepsilon_{\rm F}-\frac{eV}{2}$ is compensated.