added exercise TB_9 (bound states)

Signed-off-by: Nick Papior <[email protected]>

TB_04/run.ipynb

@@ -51,9 +51,9 @@
    "outputs": [],
    "source": [
     "device = elec.tile(15, axis=1)\n",
+    "center = device.center(what=\"xyz\")\n",
     "device = device.remove(\n",
-    "    device.close(\n",
-    "        device.center(what='cell'), R=10.)\n",
+    "    device.close(center, R=10.)\n",
     ")"
    ]
   },
@@ -70,11 +70,11 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "dangling = [ia for ia in device.close(device.center(what='cell'), R=14.)\n",
+    "dangling = [ia for ia in device.close(center, R=14.)\n",
     "                if len(device.close(ia, R=1.43)) < 3]\n",
     "device = device.remove(dangling)\n",
     "edge = []\n",
-    "for ia in device.close(device.center(what='cell'), R=14.):\n",
+    "for ia in device.close(center, R=14.):\n",
     "    if len(device.close(ia, R=1.43)) < 4:\n",
     "        edge.append(ia)\n",
     "edge = np.array(edge)\n",

TB_05/run.ipynb

@@ -7,6 +7,7 @@
    "outputs": [],
    "source": [
     "import sisl\n",
+    "import sisl.viz\n",
     "import numpy as np\n",
     "from matplotlib import animation\n",
     "import matplotlib.pyplot as plt\n",
@@ -18,11 +19,12 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "In this example, you will learn how to make use of the periodicity of the electrodes.\n",
+    "In this example, you will learn how to find and calculate properties of *bound states* in NEGF calculations.\n",
     "\n",
-    "As seen in [TB 4](../TB_04/run.ipynb) the transmission calculation takes a considerable amount of time. In this example, we will redo the *same* calculation, but speed it up (no approximations made).\n",
+    "**NOTE**: Please complete exercise [TB 5](../TB_05/run.ipynb) before doing this exercise. \n",
     "\n",
-    "A large computational effort is made on calculating the self-energies which basically is inverting, multiplying and adding matrices, roughly 10–20 times per $k$-point, per energy point, per electrode.  \n",
+    "This example is very similar to [TB 5](../TB_05/run.ipynb), with the small change that some atoms are retained in the middle of the hole.\n",
+    "You should again use the self-energies which basically is inverting, multiplying and adding matrices, roughly 10–20 times per $k$-point, per energy point, per electrode.  Please ensure \n",
     "For systems with large electrodes compared to the full device, this becomes more demanding than calculating the Green function for the system.  \n",
     "When there is periodicity in electrodes along the transverse semi-infinite direction (not along the transport direction) one can utilize Bloch's theorem to reduce the computational cost of calculating the self-energy.\n",
     "\n",
@@ -72,21 +74,30 @@
    "metadata": {},
    "outputs": [],
    "source": [
-    "H = H_elec.repeat(25, axis=0).tile(15, axis=1)\n",
-    "H = H.remove(\n",
-    "    H.geometry.close(\n",
-    "        H.geometry.center(what='cell'), R=10.)\n",
+    "H = H_elec.tile(25, axis=0).tile(15, axis=1)\n",
+    "\n",
+    "center = H.geometry.center(what=\"xyz\")\n",
+    "\n",
+    "bound_idx, ring_idx = H.geometry.close(\n",
+    "    center,\n",
+    "    R=[5., 10.]\n",
     ")\n",
+    "H = H.remove(ring_idx)\n",
     "\n",
-    "dangling = [ia for ia in H.geometry.close(H.geometry.center(what='cell'), R=14.)\n",
+    "dangling = [ia for ia in H.geometry.close(center, R=14.)\n",
     "                if len(H.edges(ia)) < 3]\n",
     "H = H.remove(dangling)\n",
-    "edge = [ia for ia in H.geometry.close(H.geometry.center(what='cell'), R=14.)\n",
+    "plot = H.geometry.plot(axes=\"xy\")\n",
+    "edge = [ia for ia in H.geometry.close(center, R=14.)\n",
     "         if len(H.edges(ia)) < 4]\n",
     "edge = np.array(edge)\n",
     "\n",
-    "# Pretty-print the list of atoms\n",
-    "print(sisl.utils.list2str(edge + 1))\n",
+    "# Pretty-print the list of atoms on the edges\n",
+    "bound_idx = H.geometry.close(center, R=5)\n",
+    "# Make sure the edge atoms are only on the hole\n",
+    "edge = np.setdiff1d(edge, bound_idx)\n",
+    "print(\"All bound-state atoms: \", sisl.utils.list2str(bound_idx + 1))\n",
+    "print(\"All edge atoms: \", sisl.utils.list2str(edge + 1))\n",
     "\n",
     "H.geometry.write('device.xyz')\n",
     "H.write('DEVICE.nc')"
@@ -98,9 +109,9 @@
    "source": [
     "# Exercises\n",
     "\n",
-    "Instead of analysing the same thing as in [TB 4](../TB_04/run.ipynb) you should perform the following actions to explore the available data-analysis capabilities of TBtrans. Please note the difference in run-time between example 04 and this example. Always use Bloch's theorem when applicable!\n",
+    "Instead of analysing the same thing as in [TB 5](../TB_05/run.ipynb) you should perform the following actions to explore the available data-analysis capabilities of TBtrans. *Remember*: always use Bloch's theorem when applicable!\n",
     "\n",
-    "*HINT* please copy as much as you like from example 04 to simplify the following tasks.\n",
+    "*HINT* please copy as much as you like from example 04/05 to simplify the following tasks.\n",
     "\n",
     "1. Read in the resulting file into a variable called `tbt`.\n",
     "2. In the following, we will concentrate on *only* looking at $\\Gamma$-point related quantities. I.e. all quantities should only be plotted for this $k$-point.  \n",
@@ -113,6 +124,7 @@
     "3. Plot the transmission ($\\Gamma$-point only). To extract a subset $k$-point you should read the documentation for the functions (*hint: `kavg` is the keyword you are looking for*).\n",
     "   - Full transmission\n",
     "   - Bulk transmission\n",
+    "   How does it compare to example 05, should it be different?\n",
     "4. Plot the DOS with normalization according to the number of atoms ($\\Gamma$ only)  \n",
     "   You may decide which atoms you examine.\n",
     "   - The Green function DOS\n",

TB_09/RUN.fdf

@@ -0,0 +1,35 @@
+TBT.HS DEVICE.nc
+
+# Play with this number to get a converged result
+TBT.k [5 1 1]
+
+# Define which physical quantites to calculate.
+# Each of these flags will decide what to calculate
+# in the calculation.
+# If you look these flags up in the manual you will
+# find the physical quantities they correspond to.
+TBT.DOS.Gf true
+TBT.DOS.Elecs true
+TBT.DOS.A true
+TBT.DOS.A.All true
+TBT.T.All true
+TBT.T.Bulk true
+TBT.T.Eig 5
+TBT.Current.Orb true
+
+# This flag is necessary to obtain the "correct"
+# bond-currents
+TBT.Symmetry.TimeReversal false
+
+%block TBT.Elec.Left
+  HS ELEC.nc
+  semi-inf-direction -A2
+  electrode-position 1
+  bloch-a1 25
+%endblock TBT.Elec.Left
+%block TBT.Elec.Right
+  HS ELEC.nc
+  semi-inf-direction +A2
+  electrode-position end -1
+  bloch-a1 25
+%endblock TBT.Elec.Right