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TP-Tight_binding/TP-Tight_binding.ipynb

@@ -115,7 +115,7 @@
     "\n",
     "In this exercise, we review the case of a monoatomic lattice, where each atoms provides 1 electrons in a $\\left|s\\right\\rangle$ local basis, which can hop directly through its direct neighbours.\n",
     "\n",
-    "<img src=\"./Figures/chain1.svg\"/>\n",
+    "<img src=\"./Figures/chain1.svg\" style=\"width: 40pc;\"/>\n",
     "\n",
     "If we only consider hopping to the first nearest neighbours and that the local state function on atom $s$ is $\\left|s\\right\\rangle$ along the chain, then the matrix elements of the monoelectronic hamiltonian are written as:\n",
     "$$\\left\\langle s \\right|H\\left| s \\right\\rangle = -\\alpha$$\n",
@@ -188,7 +188,7 @@
     "\n",
     "# add vertical lines at node positions\n",
     "for n in range(len(k_node)):\n",
-    "  ax.axvline(x=k_node[n],linewidth=0.5, color='k')\n",
+    "    ax.axvline(x=k_node[n],linewidth=0.5, color='k')\n",
     "\n",
     "ax.set_title(\"Monoatomic 1D chain with s band structure\") # put title\n",
     "ax.set_xlabel(\"Path in k-space\") # put label for the x-axis \n",
@@ -202,7 +202,7 @@
     "\n",
     "# calculate density of states and plot the density of state\n",
     "# first solve the model on a mesh and return all energies\n",
-    "kmesh=4000\n",
+    "kmesh=1000\n",
     "kpts=[]\n",
     "for i in range(kmesh):\n",
     "    for j in range(kmesh):\n",
@@ -213,8 +213,8 @@
     "print('Plotting DOS...')\n",
     "\n",
     "fig, ax = plt.subplots()  # now plot density of states\n",
-    "ax.hist(evals,200,range=(-4*gamma-alpha,4*gamma-alpha))\n",
-    "ax.set_ylim(0.0,100)\n",
+    "ax.hist(evals,150,range=(-4*gamma-alpha,4*gamma-alpha))\n",
+    "ax.set_ylim(0.0,60)\n",
     "\n",
     "ax.set_title(\"DOS for the monoatomic lattice with s electrons\") # put title\n",
     "ax.set_xlabel(\"Band energy\")\n",
@@ -299,7 +299,7 @@
     "ax.set_xticklabels(label)\n",
     "\n",
     "for n in range(len(k_node)):\n",
-    "  ax.axvline(x=k_node[n],linewidth=0.5, color='k')  # add vertical lines at node positions\n",
+    "    ax.axvline(x=k_node[n],linewidth=0.5, color='k')  # add vertical lines at node positions\n",
     "\n",
     "ax.set_title(\"DOS for the monoatomic 2x superlattice with s electrons\")  # put title\n",
     "ax.set_xlabel(\"Path in k-space\")  # put label for x-axis\n",
@@ -330,7 +330,7 @@
     "\n",
     "fig, ax = plt.subplots()  # now plot density of states\n",
     "ax.hist(evals,200,range=(-4*gamma-alpha,4*gamma-alpha))\n",
-    "ax.set_ylim(0.0,850.0)\n",
+    "ax.set_ylim(0.0,)\n",
     "ax.set_title(\"DOS for the monoatomic 2x superlattice with s electrons\")\n",
     "ax.set_xlabel(\"Band energy\")\n",
     "ax.set_ylabel(\"DOS (arb. units.)\")\n",
@@ -350,7 +350,7 @@
     "\n",
     "Starting from the previous exercise, we now consider a dimerised 1D lattice. This is straightfowardly obtained by taking the monoatomic lattice, and translating 1 atoms over 2 to the right. \n",
     "\n",
-    "<img src=\"./Figures/diatomic_chain.svg\"/>\n",
+    "<img src=\"./Figures/diatomic_chain.svg\" style=\"width: 50pc;\"/>\n",
     "\n",
     "Such a small $u$ displacement changes the way the wavefunctions overlap and hamiltonian matrixes. Now, the lattice parameter is $a' = 2a$ and the unit cell contains two atoms, and we consider two non-equivalent orbitals from which we calculate the matrix elements:\n",
     "\n",
@@ -437,7 +437,7 @@
     "ax.set_xticklabels(label)\n",
     "# add vertical lines at node positions\n",
     "for n in range(len(k_node)):\n",
-    "  ax.axvline(x=k_node[n],linewidth=0.5, color='k')\n",
+    "    ax.axvline(x=k_node[n],linewidth=0.5, color='k')\n",
     "# put title\n",
     "ax.set_title(\"Band structure for the diatomic lattice with 1s electrons\")\n",
     "ax.set_xlabel(\"Path in k-space\")\n",
@@ -577,7 +577,7 @@
     "ax.set_xticklabels(label)\n",
     "# add vertical lines at node positions\n",
     "for n in range(len(k_node)):\n",
-    "  ax.axvline(x=k_node[n],linewidth=0.5, color='k')\n",
+    "    ax.axvline(x=k_node[n],linewidth=0.5, color='k')\n",
     "# put title\n",
     "ax.set_title(\"Band structure for the graphene with $\\sf p_z$ electrons\")\n",
     "ax.set_xlabel(\"Path in k-space\")\n",