Cheese

environment.yml

name: kwant-latest
channels:
    - conda-forge
dependencies:
    - python=3.6
    - pip
    - kwant
    # required dependencies
    - numpy
    - scipy
    # optional dependencies
    - matplotlib
    - sympy
    - pip:
        - qsymm

helix.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Some experiments with kwant"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.8/site-packages/kwant/solvers/default.py:16: RuntimeWarning: MUMPS is not available, SciPy built-in solver will be used as a fallback. Performance can be very poor in this case.\n",
      "  warnings.warn(\"MUMPS is not available, \"\n"
     ]
    }
   ],
   "source": [
    "import kwant\n",
    "\n",
    "# For plotting\n",
    "from matplotlib import pyplot\n",
    "\n",
    "# For matrix support\n",
    "import tinyarray\n",
    "import numpy as np\n",
    "\n",
    "# define Pauli-matrices for convenience\n",
    "sigma_0 = tinyarray.array([[1, 0], [0, 1]])\n",
    "sigma_x = tinyarray.array([[0, 1], [1, 0]])\n",
    "sigma_y = tinyarray.array([[0, -1j], [1j, 0]])\n",
    "sigma_z = tinyarray.array([[1, 0], [0, -1]])\n",
    "\n",
    "\n",
    "def make_system(t=1.0, alpha=0.5, e_z=0.08, W=1, L=30):\n",
    "    # Start with an empty tight-binding system and a single square lattice.\n",
    "    # `a` is the lattice constant (by default set to 1 for simplicity).\n",
    "    lat = kwant.lattice.square()\n",
    "\n",
    "    syst = kwant.Builder()\n",
    "\n",
    "    #### Define the scattering region. ####\n",
    "    syst[(lat(x, y) for x in range(L) for y in range(W))] = \\\n",
    "        4 * t * sigma_0 + e_z * sigma_z\n",
    "    # hoppings in x-direction\n",
    "    syst[kwant.builder.HoppingKind((1, 0), lat, lat)] = \\\n",
    "        -t * sigma_0 + 1j * alpha * sigma_y / 2\n",
    "    # hoppings in y-directions\n",
    "    syst[kwant.builder.HoppingKind((0, 1), lat, lat)] = \\\n",
    "        -t * sigma_0 - 1j * alpha * sigma_x / 2\n",
    "\n",
    "    #### Define the left lead. ####\n",
    "    lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))\n",
    "\n",
    "    lead[(lat(0, j) for j in range(W))] = 4 * t * sigma_0 + e_z * sigma_z\n",
    "    # hoppings in x-direction\n",
    "    lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \\\n",
    "        -t * sigma_0 + 1j * alpha * sigma_y / 2\n",
    "    # hoppings in y-directions\n",
    "    lead[kwant.builder.HoppingKind((0, 1), lat, lat)] = \\\n",
    "        -t * sigma_0 - 1j * alpha * sigma_x / 2\n",
    "\n",
    "    #### Attach the leads and return the finalized system. ####\n",
    "    syst.attach_lead(lead)\n",
    "    syst.attach_lead(lead.reversed())\n",
    "\n",
    "    return syst\n",
    "\n",
    "\n",
    "def make_1D_chain(t=1.0, lambd=0.3, e_z=0.0, W=1, L=4):\n",
    "    \n",
    "    def calc_rm(m, IonsPerLaps, Laps,a=1,c=1):\n",
    "        phi_m = (m-1) * (2 * np.pi / IonsPerLaps)\n",
    "        print (\"Phi is (units of 2pi) \", phi_m/(np.pi*2))\n",
    "        return np.array([a * np.cos(phi_m), a*np.sin(phi_m), (m-1)*float(c) / (IonsPerLaps* Laps - 1)])\n",
    "    \n",
    "    def calc_vms(m,s, IonsPerLaps, Laps,a=1,c=3):\n",
    "        \n",
    "        rm = calc_rm(m , IonsPerLaps, Laps, a=a,c=c)\n",
    "        rms = calc_rm(m+s , IonsPerLaps, Laps, a=a,c=c)\n",
    "        rm2s = calc_rm(m+2*s , IonsPerLaps, Laps, a=a,c=c)\n",
    "        \n",
    "        dms = (rm - rms) / np.linalg.norm((rm - rms))\n",
    "        \n",
    "        dm2s = (rm - rm2s) / np.linalg.norm((rm - rm2s))\n",
    "        print (dms, dm2s)\n",
    "        \n",
    "        return np.cross(dms,dm2s)\n",
    "    \n",
    "    lat = kwant.lattice.square(norbs=2)\n",
    "\n",
    "    syst = kwant.Builder()\n",
    "\n",
    "    #### Define the scattering region. ####\n",
    "    syst[(lat(x, y) for x in range(L) for y in range(W))] = \\\n",
    "        2 * t * sigma_0  + e_z * sigma_z\n",
    "\n",
    "    for i in range(1,L):\n",
    "        syst[lat(i,0), lat(i-1,0)] = -t * sigma_0 \n",
    "\n",
    "    for i in range(2,L):\n",
    "        # vms is 1 based so we need i+1, also we set L=4 sites in 1 loop (hard coded as the last parameter)\n",
    "        d = calc_vms(i+1, 1, L, 1)\n",
    "        syst[lat(i,0), lat(i-2,0)] = 1j * lambd * (sigma_x * d[0] + sigma_y*d[1] + sigma_z*d[2])\n",
    "\n",
    "\n",
    "    #wrapped = kwant.wraparound.wraparound(syst).finalized()\n",
    "    #kwant.wraparound.plot_2d_bands(wrapped,kx=1)\n",
    "\n",
    "    #### Define the left lead. ####\n",
    "    #   https://kwant-discuss.kwant-project.narkive.com/ZRoAKlBg/up-down-conductance\n",
    "    lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)), conservation_law = -sigma_z )\n",
    "\n",
    "    lead[(lat(0, j) for j in range(W))] = 2 * t * sigma_0  + e_z * sigma_z\n",
    "    # hoppings in x-direction\n",
    "    lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \\\n",
    "        -t * sigma_0\n",
    "\n",
    "    #### Define the right lead. ####\n",
    "    #rlead = kwant.Builder(kwant.TranslationalSymmetry((1, 0)))\n",
    "\n",
    "    #rlead[(lat(L, j) for j in range(W))] = 0 * t * sigma_0  + e_z * sigma_z\n",
    "    # hoppings in x-direction\n",
    "    #rlead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \\\n",
    "    #    -t * sigma_0\n",
    "\n",
    "    #### Attach the leads and return the finalized system. ####\n",
    "    syst.attach_lead(lead)\n",
    "    rlead = lead.reversed()\n",
    "    syst.attach_lead(rlead)\n",
    "\n",
    "    return syst, lead, rlead\n",
    "\n",
    "\n",
    "\n",
    "def make_3D_rchain(t=1.0, t_so=3, e_z=0.0):\n",
    "    \"\"\"\n",
    "    A 3D linear chain forming a spiral.\n",
    "    Notice the huge value for t_so!\n",
    "    \"\"\"\n",
    "    \n",
    "    # These are the bravais vectors, an orthorombic cell\n",
    "    vecs= [np.array([2,0,0]),np.array([0,2,0]),np.array([0,0,2*np.pi])]\n",
    "\n",
    "    # this function creates a spiral\n",
    "    def RC(R,gamma,phi):\n",
    "        return R*np.array((1.+np.cos(phi),1.+np.sin(phi),gamma*phi))\n",
    "    \n",
    "    # Here we set the basis functions for each sublattice\n",
    "    bases=np.zeros([10,3])\n",
    "    for i,p in enumerate(np.linspace(0,2*np.pi,10)):\n",
    "        bases[i] = RC(1,1.,p)\n",
    "    \n",
    "    \n",
    "    lat = kwant.lattice.general(prim_vecs=vecs,norbs=2,basis=bases)\n",
    "    syst = kwant.Builder()\n",
    "\n",
    "    #### Define the scattering region. ####\n",
    "    for i in range(10):\n",
    "        slat = lat.sublattices[i]\n",
    "        syst[slat(0,0,0)] = 2 * t * sigma_0  + e_z * sigma_z\n",
    "\n",
    "    for i in range(1,10):\n",
    "        slat1 = lat.sublattices[i]\n",
    "        slat0 = lat.sublattices[i-1]\n",
    "        \n",
    "        sx,sy,sz = np.cross([0,0,1],bases[i]-bases[i-1])\n",
    "        \n",
    "        syst[kwant.builder.HoppingKind((0,0,0), slat0, slat1)] = \\\n",
    "        -t * sigma_0 - 1.j * t_so * (sx*sigma_x + sy*sigma_y * sz*sigma_z)\n",
    "\n",
    "\n",
    "    #### Define first lead. ####\n",
    "\n",
    "    sym_lead1 = kwant.TranslationalSymmetry((0, 0, -1))\n",
    "\n",
    "    lat_lead = kwant.lattice.cubic(norbs=2)\n",
    "    \n",
    "    lead1 = kwant.Builder(sym_lead1, conservation_law = -sigma_z )\n",
    "    lead1[(lat_lead(2, 1, -1) )] = 2 * t * sigma_0\n",
    "    lead1[lat_lead.neighbors()] = -t * sigma_0\n",
    "\n",
    "\n",
    "    \n",
    "    syst[lat_lead(2,1,-1)] = 2 * sigma_0\n",
    "    syst[lat_lead.neighbors()] = -1 * sigma_0\n",
    "    \n",
    "    syst[((lat_lead(2, 1, -1), lat.sublattices[0](0,0,0)) for i in range(1))] =  -t * sigma_0\n",
    "    syst.attach_lead(lead1)\n",
    "    \n",
    "    \n",
    "    #### Define second lead. ####\n",
    "\n",
    "    sym_lead2 = kwant.TranslationalSymmetry((0, 0, 1))\n",
    "\n",
    "    lat_lead2 = kwant.lattice.cubic(norbs=2)\n",
    "    \n",
    "    lead2 = kwant.Builder(sym_lead2, conservation_law = -sigma_z )\n",
    "    lead2[(lat_lead2(2, 1, 2*np.pi+1) )] = 2 * t * sigma_0\n",
    "    lead2[lat_lead2.neighbors()] = -t * sigma_0\n",
    "\n",
    "\n",
    "    \n",
    "    syst[lat_lead2(2,1,2*np.pi+1)] = 2 * t * sigma_0\n",
    "    syst[lat_lead2.neighbors()] = -t * sigma_0\n",
    "    \n",
    "    syst[((lat_lead2(2, 1, 2*np.pi+1), lat.sublattices[-1](0,0,0)) for i in range(1))] = -t * sigma_0\n",
    "    syst.attach_lead(lead2)\n",
    "\n",
    "    return syst, lead1, lead2\n",
    "\n",
    "\n",
    "def make_simple_system(t=1.0, alpha=0.5, e_z=0.01, W=1, H=10, L=24):\n",
    "    lat = kwant.lattice.square()\n",
    "\n",
    "    syst = kwant.Builder()\n",
    "\n",
    "    #### Define the scattering region. ####\n",
    "    syst[(lat(x, y) for x in range(L) for y in range(W))] = 0 * t\n",
    "    # hoppings in x-direction\n",
    "    for i in range(1,L):\n",
    "        syst[lat(i,0), lat(i- 1,0)] = -t\n",
    "\n",
    "\n",
    "    #### Define the left lead. ####\n",
    "    lead = kwant.Builder(kwant.TranslationalSymmetry((-1, 0)))\n",
    "\n",
    "    lead[lat(0, 0)] = 0 * t\n",
    "    # hoppings in x-direction\n",
    "    lead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \\\n",
    "        -t\n",
    "\n",
    "    #### Define the right lead. ####\n",
    "    rlead = kwant.Builder(kwant.TranslationalSymmetry((1, 0)))\n",
    "\n",
    "    rlead[lat(L, 0)] = 0 * t\n",
    "    # hoppings in x-direction\n",
    "    rlead[kwant.builder.HoppingKind((1, 0), lat, lat)] = \\\n",
    "        -t\n",
    "\n",
    "    #### Attach the leads and return the finalized system. ####\n",
    "    syst.attach_lead(lead)\n",
    "    syst.attach_lead(rlead) #.reversed())\n",
    "\n",
    "    return syst, lead, rlead\n",
    "\n",
    "def plot_conductance(syst, energies):\n",
    "    # Compute conductance\n",
    "    data = []\n",
    "    for energy in energies:\n",
    "        smatrix = kwant.smatrix(syst, energy)\n",
    "        #data.append(smatrix.transmission(1, 0))\n",
    "        data.append(smatrix.transmission((1, 0), (0, 0)))\n",
    "\n",
    "    #pyplot.figure()\n",
    "    pyplot.plot(energies, data)\n",
    "    for energy in energies:\n",
    "        smatrix = kwant.smatrix(syst, energy)\n",
    "        #data.append(smatrix.transmission(1, 0))\n",
    "        data.append(smatrix.transmission((1, 0), (0, 1)))\n",
    "\n",
    "    #pyplot.figure()\n",
    "    pyplot.plot(energies, data)\n",
    "    pyplot.xlabel(\"energy [t]\")\n",
    "    pyplot.ylabel(\"conductance [e^2/h]\")\n",
    "    pyplot.show()\n",
    "\n",
    "\n",
    "def plot_spin_conductance(syst, energies):\n",
    "\n",
    "\n",
    "    data = []\n",
    "    for energy in energies:\n",
    "        smatrix = kwant.smatrix(syst, energy)\n",
    "        data.append(smatrix.transmission(1, 0))\n",
    "\n",
    "    #pyplot.figure()\n",
    "    pyplot.plot(energies, data)\n",
    "    pyplot.xlabel(\"energy [t]\")\n",
    "    pyplot.ylabel(\"conductance [e^2/h]\")\n",
    "    pyplot.show()\n",
    "\n",
    "    data = []\n",
    "\n",
    "    data_upup = []\n",
    "    data_updn = []\n",
    "    data_dnup = []\n",
    "    data_dndn = []\n",
    "    for energy in energies:\n",
    "        smatrix = kwant.smatrix(syst, energy)\n",
    "        data_upup.append(smatrix.transmission((1, 0), (0, 0)))\n",
    "        data_updn.append(smatrix.transmission((1, 1), (0, 0)))\n",
    "        data_dnup.append(smatrix.transmission((1, 0), (0, 1)))\n",
    "        data_dndn.append(smatrix.transmission((1, 1), (0, 1)))\n",
    "\n",
    "    pyplot.figure()\n",
    "    pyplot.plot(energies, data_upup,label='up -> up',ls='-')\n",
    "    pyplot.plot(energies, data_dndn,label='dn -> dn',ls='--')\n",
    "    pyplot.legend()\n",
    "\n",
    "    pyplot.figure()\n",
    "    pyplot.plot(energies, data_dnup,label='dn -> up',ls='-.')\n",
    "    pyplot.plot(energies, data_updn,label='up -> dn',ls=':')\n",
    "    pyplot.legend()\n",
    "    \n",
    "    pyplot.xlabel(\"energy (t)\")\n",
    "    pyplot.ylabel(\"spin conductance (e^2/h)\")\n",
    "    pyplot.show()\n",
    "\n",
    "def plot_bands(syst):\n",
    "    bands  =  kwant.physics.Bands( syst )\n",
    "    ks=np.linspace(-np.pi,np.pi,num=101)\n",
    "    energies=[bands(k) for k in ks]\n",
    "    f,ax=pyplot.subplots()\n",
    "    ax.plot(ks,energies,'k')\n",
    "    pyplot.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "here we define a system..."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Phi is (units of 2pi)  0.5\n",
      "Phi is (units of 2pi)  0.75\n",
      "Phi is (units of 2pi)  1.0\n",
      "[-0.57735027  0.57735027 -0.57735027] [-7.07106781e-01  1.29893408e-16 -7.07106781e-01]\n",
      "Phi is (units of 2pi)  0.75\n",
      "Phi is (units of 2pi)  1.0\n",
      "Phi is (units of 2pi)  1.25\n",
      "[-0.57735027 -0.57735027 -0.57735027] [-1.73191211e-16 -7.07106781e-01 -7.07106781e-01]\n"
     ]
    }
   ],
   "source": [
    "#syst=make_simple_system()\n",
    "syst, llead, rlead  = make_1D_chain(e_z=0.)\n",
    "#syst, llead, rlead  = make_3D_rchain(e_z=0.)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Check that the system looks as intended."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/lib/python3.8/site-packages/kwant/_plotter.py:70: RuntimeWarning: plotly is not available, if other engines are unavailable, only iterator-providing functions will work\n",
      "  warnings.warn(\"plotly is not available, if other engines are unavailable,\"\n"
     ]
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXIAAAB/CAYAAADyzUljAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4yLjIsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+WH4yJAAATh0lEQVR4nO3deXhdVbnH8e+bsUPSKUnpFBo6U0oLJRZKmRUsReB6uV6FAnIZigMqFxCVQS5XUK+oyKPcxwuKqCACIpMyWAYFFGjTuTVtKUVom9IkdEjakLRN1v1jB56SJidnWCc7C3+f5+nTJj3nPW9Pd35777XXWducc4iISLhy4m5AREQyoyAXEQmcglxEJHAKchGRwCnIRUQCpyAXEQlcXhwvWlpa6ioqKuJ4aRGRYC1atKjeOVfW8ftegtzM7gI+AdQ656Z09/iKigqqqqp8vLSIyD8NM3uzs+/7Glq5G5jtqZaIiKTAS5A7514AtvqoJSIiqemxi51mNs/Mqsysqq6urqdeVkTkQ6/Hgtw5d4dzrtI5V1lWtt9YvYiIpEnTD0VEAqcgFxEJnJcgN7P7gJeBiWa20cwu8lFXRES652UeuXPubB91REQkdRpaEREJnIJcRCRwCnIRkcApyEVEAqcgFxEJnIJcRCRwCnIRkcApyEVEAqcgFxEJnIJcRCRwCnIRkcApyEVEAqcgFxEJnIJcRCRwCnIRkcApyEVEAqcgFxEJnIJcRCRwCnIRkcApyEVEAqcgFxEJnIJcRCRwCnIRkcApyEVEAqcgFxEJnIJcRCRwCnIRkcDlxd1At7Zvh3fegcZGaG6OvpefD0VFMGgQlJVBTi/ZH+3YAc8+C6tWweuvw65dUFAA5eUwcSKceCJUVMTd5fv+9no9z1bXsmLTDjZtexfnHEOKCpgyYiAzx5Ywe8owCvNy424TgHd2tvDo0hoWv7WN1W83sqtlLwV5OYwrK2LqqEGcPm04Y8qK4m4TAOccL62r57nVtazctIOa7c045ygtLuSQEQOZNa6Ejx8yjPzc3rHd1jY289jSGpa8tZ3qtxtoammlT34O44YWM23UQM44bASjS/rH3WakrQ0WLoRXX4W1a6GuLvr+kCEwYQIccQTMmgW5vWO7paUFamuhoSHKg9bWqLd+/WDAABg6FPr0yfhlzDnnodvUVFZWuqqqqsQP2roV1q+P/vGJ5OXBqFFRWMYV6Dt3wp13wlNPwe7diR97+OHwpS/BQQf1TG+deLZ6C995cjXrancmfFxJ/wIuOW4Mlxw7htwc66HuPmh7026+88RqHl66id1727p8nBkcO76MG06fzNgYA/2plZv53lNrWF+feLstLSrkCyeM5YKjK8iJ6b2t39nCt5+o5vFlNexp7ToHzOCkiUP55umT4w30Z5+Fu+6CmprEjysthXPPhTPOiJqPQ0tLlF91ddBdxpaUwLhxSQW6mS1yzlXu9/1eF+RtbbBuHWzenFrRoiKYPBn69s28wVQsWwY33QT19ck/Jz8fLroIPv3p7PXViZa9rVzz+5U8tHhjSs+bNmogt8+dzqjB/bLUWedeeq2ey+9fSv3OlqSfU5iXwzVzDuazR1dkr7FOvLu7lasfWs7jy7oJmQ4qRw/m9rnTOWBA5kdlqXhu9RauenA5W3d1c+Cxj775udxw+mQ+M+PALHbWiaYm+O534cUXU3ve4YfD9dfD4MHZ6asrdXXR2cLevck/JzcXxo+HAw5I+LAwgrytDf7+92goJR0FBTBtWnTa0hMWLYJrrun+KLwrZ58N8+b57akLLXtbufiXVbz4Wgo7nH2MGNiH+y+dSfmQnnlvn63ewufvWczu1q6PwhO54uQJfPmj4z131bnmPa2cf9cCFryxNa3nHzikHw9cOpNhA3smzJ9YsZkv37eEvW3p/exfM2cS844b67mrLjQ1wVVXQXV1es8vL4fbbuu5MN+yBVavTv/548bByJFd/nVXQd47Bune88Yb6Yc4RIG6alW0Q8i22lq44Yb0QxzgvvvgmWf89ZTAzX+sTjvEAWp2NDPv14vYk2awpuIf9bu47DdL0g5xgB/OX8tTK9/22FXXrn9kZdohDvDW1iY+d88iWtMM1lSs3dLI5fcvTTvEAb79xGr+srbOY1cJfP/76Yc4wIYNcOON3Q9v+NDYCGvWZFZj3broumCKek+QNzTAxtRO+TvV1BTtELLtllu6H79Pxo9/HF0PyKJX1r/Dr195M+M61Zsb+Mlz6zx01DXnHFf/bjnv7mnNuNZ1j6xke1MGO9okPL+mlgcXZb7dLt2wnTtfXO+ho661tTm++uCyhNcakvX1h5bT2LzHQ1cJvPACPP985nWWLYNHHsm8TiJtbVGI+9hhrFkTXRRNQe8J8jczD5r31dTAnixuZCtWQHcXa5PV0AAPPeSnVhdunb/W2wHJz15cz86WFMb+UvTSunoW/MPPjq1+Zwu/ftnjdtWJH81f663WT//yOs0edmBdeaZ6C8s27vBSa/OOZu5fuMFLrS7dfbe/Wvfck9qYdarq6/0c2EE0O2/LlpSe4iXIzWy2ma0xs3Vm9vWUCzQ3+z0qbWuDt7N4Wv34437rPflk1jaydbWNvJrBaX9Hu3a38nCKF0tTce8rb3mtd9+Ct2jL0pDFyk07vAUjwPamPSlfLE3Fva/6fW991/uAFSv8nllv3Zr6xdJUdDeTJsv1Mp5Hbma5wO3AycBGYKGZPeac+3vSRbZty7SN/dXXZ+8Cx8KFfutt2xadRmZhjvmLK/0P29z/l+X0q1nkva5z8OfVhYC/KWM1O5q5/vu3U5Lnf4ilatcQoMxrzd88t4ScNxd4rQnQ6uCvr/l9b9+o38WGZaspLy7wVvN98+f7r/nKK/CRj/iv29YWfYbEp127outvBcm9tz4+EDQDWOecWw9gZr8FzgSSD/Kdieczp6WhIZpVko26aVyM6Na3vuW/JrByzGwom+K15tK33uHfvnGh15oAeYOGM/LSO73Xve1Xv2fXKg9jrR2UnnE1/Q/2G+QLXqvhka993mtNgPyyCkZc+BPvdVfe+EPKt73mvW5WLF+enUzIlsbGaI55EnwMrYwE9h0s29j+veS1JD9POHaNjXF3kJLaAv8fjsntP8R7TYDcoizVzVq/yf2QpVYzrPc2G9tX1mTjgDGbUpgR5yPIOztX229Q0szmmVmVmVXV1fXQ1CURkX8CPoJ8I1C+z9ejgP1G6p1zdzjnKp1zlWVlHU5HCws9tNFDBgyIu4OUDGvxfwbR2pj+fPQ46u4NqN/s9ZrB5zMSGLY7oDPUwH52U8lFH2PkC4HxZnYQsAn4DHBOShWKiz200cGAAdFHXrPhF7/wP/f7m9+E0aP91gQOXbWVB/+a2lSm7kw/qIzbfvc7rzXfc91ix7utftfHuOKCsxicd4bXmgCLmwbzkuez9ZkTR3FOFt7bNgfXLnbsbvP73h76X1dBUb7XmgA89hg8+qjfmlOnRotq+dbWBkuW+K+bQi5mHOTOub1mdhnwNJAL3OWcW5VSkWzMLikri9ZfyYYZM6IFsnwpLYXjjsvKim3HDTgA+9sWrx9sO+fEwzgrS+ttPN+ymD8sT3GdnQQOHNKP//7qZVgWFk9a/XYDs3/kd0rb+ScfwZmHpXaJKVlP71rIM9W13uqNH1rEiKkTvdX7gFNO8R/ks2ZlLxMGDfI7CaK4OFqTKUle5pE7555wzk1wzo11zt2ccoHCwqSvziYlJweGDfNXr6Mzz/Rb77TTsrbsZkVpf44ZV+qtXnGfvKwFDcC5R/k9KznnyAOzEuIAk4YNoHK0v4OQkv4FnDpluLd6Hc31/N76/r/6gMmT/Z5Rl5XBzJn+6nU0YoTfesNT2w56zyc7Kyr8LTlZXh4tb5stkyZFe3cfBg+GT37ST60u/OfJE/C1UuoXTxxH34LsrfV81JgSjh3vZ8czYmAf5h6Z3ZX6rjxlorfN9ssfHU9BXvZ+JE+YUMaMCj+zV0aX9OPfK8u7f2AmLrrIX60LLsjuGuWlpf6GiPv163YVxI56T5AXFcGBHn7ofNXpzhVX+Ll4csUVMHBg5nUSmH7gYC45bkzGdQ4rH8Qlx2Zepzv/c9ZUigsz2xGbwXfOmkpxnyyM3+5j5tgSzvdwZHrUmCGcPzOLR7iAmXHLp6bSL8MdcY7B986amtUdOgBHHgmnnuqnzpw5mddJxCy6eYyPvfrEiSnfW6H3BDlEF/uGDk3/+YWFcMghPXODiSFD4OabM1v//OKL4Zhj/PWUwFdPmcjHD0ltL7+vg0r7c8d5R/TIDSZGDOrL/51/BH3z0w+K60+bzPET/H5YpyvXnjaZEyam/1rjhxbxv3OPyNoQ0L5Gl/Tn9rnT0z7yN4Ob/uVQjhzjfw59py6/PFpXPF3jxsF11/nrJ5H+/aMhoUz+HydNSusAsXcFuVn0DylP45RtwIDoP9zDbZOSNmUK3HprdIeiVPTpA1deCXPnZqevTuTl5nD7OdP5j1kVKW9nR48t4YFLZzK0B29+cPTYUu65+EhGDU5tR1lUmMcPPjWNC4/puTswFeTlcMd5lZyTxjDO8RPKeODSmQzpn4WPuXfhxIlD+dWFMxie4vrnA/rk8eOzD0/r35m2goLophKzZ6f+3KOPjn4+s3WBszOlpVEuJPnR+vfl5UUHoSkOqbynd91YYl87dkS3SmpoSPy4wsIo+EeMiPe2Tr/8ZTRlKtEKaDk50dj65z7n/+JICl5Z/w7ffXI1Szckvso+clBfvnDiWM6Zkb0Lht3Z1bKXW+ev5bcLNyRcdTEvx/j4IcO45rSDGTmoh+8StY8XX6vje0+tYcWmxGtvHDikH5edNC7748wJNDTv4QdPr+HBRRtp2t31qov5ucacQ4dzzZyDe/xORh/w8svw859H98NNpLwczjsPTj65Z/rqzJ490aJfW7Ykvj+CWTQKMWZMUuEfxh2COrNz5/43X87Liy4sDBwYzXaJK8A7am6OFr/a9+bL+fnRhjVpEhx/fGZDR56t3LTj/Zsvb9zWhHNQUlTAlJEDmTmmhOMnlMV2P8mOdrXs5YkVm1myYTvVmxv2u/nyaVOHxxsyHSzbsP39my9v2v4uzkFpcfTeHj22lOPGl8a2c+yosXkPT6zYzNIN26ne3EjT7r0U5uUyfmgR08oHMefQ4ZQV96IP7a1a9cGbLzsX5cCECTB9evSrl7y37NkT9djYuP/Nl4uLo9k0KRy9hxvkIiIChHKrNxERSZmCXEQkcApyEZHAKchFRAKnIBcRCZyCXEQkcApyEZHAKchFRAKnIBcRCZyCXEQkcApyEZHAKchFRAKnIBcRCZyCXEQkcApyEZHAKchFRAKnIBcRCZyCXEQkcApyEZHAKchFRAKnIBcRCZyCXEQkcApyEZHAKchFRAKnIBcRCZyCXEQkcApyEZHAKchFRAKXUZCb2afMbJWZtZlZpa+mREQkeZkeka8E/hV4wUMvIiKShrxMnuycqwYwMz/diIhIynpsjNzM5plZlZlV1dXV9dTLioh86HV7RG5mzwDDOvmra51zjyb7Qs65O4A7ACorK13SHYqISELdBrlz7mM90YiIiKRH0w9FRAKX6fTDT5rZRmAm8Ecze9pPWyIikixzrueHq82sDngzzaeXAvUe28m2kPoNqVcIq9+QeoWw+g2pV8is39HOubKO34wlyDNhZlXOuWA+fBRSvyH1CmH1G1KvEFa/IfUK2elXY+QiIoFTkIuIBC7EIL8j7gZSFFK/IfUKYfUbUq8QVr8h9QpZ6De4MXIREfmgEI/IRURkH0EGuZndYmarzWy5mT1sZoPi7qkroSz1a2azzWyNma0zs6/H3U8iZnaXmdWa2cq4e+mOmZWb2fNmVt2+HXwl7p66YmZ9zGyBmS1r7/XGuHvqjpnlmtkSM/tD3L10x8z+YWYrzGypmVX5rB1kkAPzgSnOuanAWuAbMfeTSK9f6tfMcoHbgVOBycDZZjY53q4SuhuYHXcTSdoLXOmcOxg4CvhiL35vW4CTnHPTgMOA2WZ2VMw9decrQHXcTaTgROfcYZp+CDjn/uSc29v+5SvAqDj7ScQ5V+2cWxN3H92YAaxzzq13zu0GfgucGXNPXXLOvQBsjbuPZDjnNjvnFrf/uZEodEbG21XnXGRn+5f57b967UU0MxsFnAb8LO5e4hZkkHdwIfBk3E0EbiSwYZ+vN9JLwyZkZlYBHA68Gm8nXWsfqlgK1ALznXO9tlfgR8DVQFvcjSTJAX8ys0VmNs9n4YxuLJFNySyfa2bXEp263tuTvXXka6nfGHV2Z5BeeyQWIjMrAh4CLnfONcTdT1ecc63AYe3XnR42synOuV53LcLMPgHUOucWmdkJcfeTpFnOuRozGwrMN7PV7WeXGeu1Qd7d8rlm9lngE8BHXcxzKD8ES/1uBMr3+XoUUBNTLx86ZpZPFOL3Oud+H3c/yXDObTezPxNdi+h1QQ7MAs4wszlAH2CAmd3jnDs35r665Jyraf+91sweJhrS9BLkQQ6tmNls4GvAGc65prj7+RBYCIw3s4PMrAD4DPBYzD19KFh0H8SfA9XOuR/G3U8iZlb23gwwM+sLfAxYHW9XnXPOfcM5N8o5V0G0vT7Xm0PczPqbWfF7fwZOweMOMsggB34CFBOdniw1s5/G3VBXQljqt/3C8WXA00QX4x5wzq2Kt6uumdl9wMvARDPbaGYXxd1TArOA84CT2rfVpe1Hkb3RcOB5M1tOtHOf75zr9dP6AnEA8JKZLQMWAH90zj3lq7g+2SkiErhQj8hFRKSdglxEJHAKchGRwCnIRUQCpyAXEQmcglxEJHAKchGRwCnIRUQC9/+mevHHJ8299QAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kwant.plot(syst)\n",
    "\n",
    "# Finalize the system.\n",
    "syst = syst.finalized()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Plot bands in the lead"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_bands( llead.finalized() )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "eventually plot spin conductance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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X7ucpP0k3jlBKxd6wiWfiGaF1wwK/Uwl+Qa9es5jR2R5FWSl+p6KUCqCs7Dw2WyWk1lT6nUrwC/pVm2/mv8KP+J2GUirAajInMKx9JcbzfM0j0AV9544tDDG1RAZP8TsVpVSANY66hF9HL6KqrtnXPAJd0KuWvw1Azqj+s3iOUip4Bk86n9nuBby/vdXXPAJd0Ns3zidqLMomnu53KkqpABszOJNhdj3bVvm7aU+gb/3P3FnJRrucUWn9YyU0pVQwJdkhZqU8iFkTAj7rWx69GqGLyPkislpE1orIzQc5ni0ic0XkfRFZISJXxT7VI+N6hh93XM6b5d/xOxWlVAJoyJtIWWQNTjTiWw49FnQRsYAHgQuA8cAMERm/32nXAyuNMScC04H/FpGkGOd6RNbVtrC4s4Tccef4mYZSKkHYpRWkSoRNq5b4lkNvRuinAGuNMeuNMRFgDnDRfucYIFO6dk7OAOoBJ6aZHqHN77/JZ0PvMKlEp1uUUn0vZ9jxADRuW+NbDr0p6MXAlr0eV3U/t7cHgHHANmA58G1jzAENmSJyjYgsEpFFtbW1R5ly72StmsOdSbMpL8jq0zhKKQVghbtuXjRuP55yAQ62rbXZ7/F5QCUwFJgEPCAiB1RSY8wsY0yFMaaisLDwiJM9EgUNy9mUMo6QFehGHqVUP2GyS5kZ+Xdqcv2776U31a4KKN3rcQldI/G9XQU8bbqsBTYAvu223NbSyHB3E62Fk/xKQSmVYOyUTN7wTqIlnO9bDr0p6AuBUSJS3n2h8zLg2f3O2Qx8DEBEBgFjgPWxTPRINOzcgSUGO3eYXykopRKMbTr5ZGghyS1bej65r3Lo6QRjjCMiNwAvAxbwmDFmhYhc2338YeBO4HERWU7XFM0PjTE7+zDvw3KdrjkssX1ttFFKJZCw08yspF8wvzoN8Odmxl7dWGSMeQF4Yb/nHt7r+23AJ2Ob2tHrSC/h5I6HuKP4VL9TUUoliLDdtd+C8aK+5RDIK4ZRY1FLDqHkNL9TUUolCCsc7vrG1YIeU9K8le/afyardZPfqSilEsTuHdGMFvTYkqat3GT/nYy2Kr9TUUolCNvuHqF7/t1TGciC7jldvyFDuz9gpZTqY5Zl86XOH/FBwad8yyGgBb2ryyWkXS5KqTiRUIilofHUhwf5lkMgC7qrI3SllA8+a71LUeNy3+IHsqB73RclLB2hK6Xi6Meh3zJu58u+xQ9kQd9RdBbjOh4jWjjR71SUUgnExUa0Dz22oiZEOymEw4HekEkp1c84WIh2ucRW5s73+ZH9BEmRXX6nopRKIF0jdC3oMZXeuIar7RcJu+1+p6KUSiCOWIjxr6AHck5i951au+/cUkqpeLgt9RaG5hVS4VP8QBd0S9sWlVJxtC2pDDvk3xpSgSzodG8BZYV1hK6Uip9pzr9Ib0kHn8bogSzonte1nWk4rCN0pVT8fL7jGTqdDOAmX+IH8qLokuIvU9bxJHZyht+pKKUSiCc2lna5xFbUNYAQtgP59pRS/ZQrNiEfu1wCWfGOq32Fu8OPIiJ+p6KUSiBeyN+CHsg59EFNKzgx9LbfaSilEownNpYW9BjzojhYfmehlEowfyj8Htsa2vijT/EDWdDFc3AkkG9NKdWPtSUXUG2afYsfyKonXhRXR+hKqTg7oW0+Izs3AtN9iR/Ii6JRbFok3e80lFIJZnLLm1weedq3+IEcof+l6Nss6WjgLb8TUUollpCNhbYtxlTUM9iWtiwqpeLLhGwsXN/iB3KEfu7OP3F25078msdSSiWokI2tBT22RrQvI8Ot9TsNpVSCMaEwtt4pGlsh4+CJdrkopeLrndJvMN15wLf4gS3orvahK6XizCRlUOv512EXzILuOXha0JVScTa8aQnft+bgOv5Mu/SqoIvI+SKyWkTWisjNhzhnuohUisgKEXkztmkemSbJpMnO8zMFpVQCKm5dzvX2s0Sjnb7E73EYKyIW8CDwCaAKWCgizxpjVu51Tg7wEHC+MWaziBT1VcK9cVfmrRRkJHGan0kopRKOWF2b6jjRCKTGf+qlNyP0U4C1xpj1xpgIMAe4aL9zLgeeNsZsBjDG1MQ2zSMTdT1sK5CzSUqp/izUVdDdaMSf8L04pxjYstfjqu7n9jYayBWRN0RksYh89WAvJCLXiMgiEVlUW9t3bYU3tP6aTzf+qc9eXymlDmb3CD3qU0HvzZXDg91yaQ7yOlOAjwGpwLsi8p4x5qN9fsiYWcAsgIqKiv1fI2YmOcvZEfGvuV8plZh2F3TX6b8j9CqgdK/HJcC2g5zzkjGm1RizE3gLODE2KR452ziYkG4QrZSKr83DLmZ0x++IpA72JX5vCvpCYJSIlItIEnAZ8Ox+5/wDOEtEbBFJA6YCH8Y21d6zcDAhbVtUSsWXHU4mQpio12cTEIeP39MJxhhHRG4AXgYs4DFjzAoRubb7+MPGmA9F5CVgGeABvzXGfNCXiR+OjasFXSkVd7nNq7ndfhzTPBoKR8U9fq+qnjHmBeCF/Z57eL/H9wH3xS61o7eZQbQk+do5qZRKQJntVcy0/8na1u8C8S/ogeztu8z9Ce+VXOV3GkqpBBOykgDw+nHb4oDjeNqHrpSKP7G7mjG8ftzlMqAYz+NP1o+ZVDvX71SUUgnGsne3LUZ9iR+4gu66DhWhj8hydvqdilIqwYiVRMRYeG4/XpxrIHF2z11pl4tSKs46hk5ldOcT1BWd6kv8wBX0aKRrlbPdd2wppVS8hLv3MnZcf/rQA1fQ94zQtaArpeIspa2a++yHSd9Z6Uv84BV0z7DUG0lnqvahK6XiK9lt4Yv2WyQ1b+n55D4QuIIeSc7lksh/sn3oeX6nopRKMKFwVx+6cbXLJSYc1wMgrH3oSqk4s+zuG4u0oMeG2bWJF5N+yNCd8/xORSmVYOzdI3TtQ48N09nMuNAWkr12v1NRSiUYK5xEg0nH9am0Bq6g775DS9sWlVLxZmcUManzET4ccrEv8YNX0LvbFkPdc1lKKRUv9p4+dM+X+IEr6LsvRoRsHaErpeLLFpeHwvczvPoVX+IHrqB3WunMc4/HS833OxWlVIIJWzafshaQ3bLOl/iBK+hNWWO4InoL0cIJfqeilEowIcvCNQLathgbjtc1d6XroSul/OBgg6cFPSaytr7F20nfJr1xrd+pKKUSkIOFeLp8bkxIZzOloVrswL0zpdRAsFWKaJc0X2IHbtHw3WsoWGHtclFKxd/l9s/55KDBnOND7MCNY3fv5WfbyT5nopRKRHYo5FsfeuBG6OgIXSnlo9vcX+NVjwJOjHvswI3Qm5IH8U93ClZyht+pKKUS0ERvNUM6/GnKCNwIfXPu6fxnNIfK9Fy/U1FKJSBXtMslZrQPXSnlJxcbMVrQY2L8pj+wOPmb2F7E71SUUgnIExvLpxuLAjflYkVbyZdm3LCutqiUir9tdjGOle5L7MAVdLwonhEsO3hvTSnV/z2YezOhEHzMh9iBm3LBdXCw/M5CKZWgbEtwXONPbF+i9iHxojhY6ISLUsoPX2maRTjaBJwe99i9GqGLyPkislpE1orIzYc572QRcUXkC7FL8chsTR3D83KWX+GVUgluiLOVsuh6X2L3WNBFxAIeBC4AxgMzRGT8Ic67F3g51kkeicXZH+e/rGv9TEEplcBMyMY2/Xf53FOAtcaY9caYCDAHuOgg590I/A2oiWF+R8xxvT37+imlVLx5YmP14z70YmDLXo+rup/bQ0SKgUuAhw/3QiJyjYgsEpFFtbW1R5prr3x+yz38OXpTn7y2Ukr1xAuFsXB9id2bgn6w4e7+l3DvB35ojDnsuzDGzDLGVBhjKgoLC3ub4xGxvAgW/qx0ppRSO1OG8ZGU+RK7N10uVUDpXo9LgG37nVMBzBERgALgUyLiGGP+HpMsj0DIi+JK4Jp3lFIDxFuDZ/LqrhoW+hC7N5VvITBKRMqBrcBlwOV7n2CMKd/9vYg8DjznRzEHEOPgivahK6X80a/XQzfGOCJyA13dKxbwmDFmhYhc2338sPPm8dY1Qte10JVS/phW+0e+5L4EfDLusXs1N2GMeQF4Yb/nDlrIjTEzjz2to7c0ZSoSbWOUn0kopRJWptvAyH36SOIncJPNL6ZeiEmFK/1ORCmVkEzIxu7HXS4DixshKaRdLkopn1hhwuJivPjXocCN0H9S/z3a7BzgVb9TUUololBXWXWcKOGk+G5WH7gResg4eKHA/Z5SSg0QzenDecM9EceJ/7RL4Aq6ZRyMdrkopXyyecj5zIz+kGgo/nUogAXd1RG6Uso3dqjr5no/1kQPXkHHwWhBV0r5ZGT1i7yTfANu0464xw5cQX86dB6rss7wOw2lVIJKMhGGSj1utDPusQM3lH1cLuKTeYP9TkMplaisrrlz14nEPXTgRuhpThNpxP83o1JKAYSsrnGy68R/k4vAFfQXzXV8fMcjfqehlEpQYnXtaKwFPQZsXL0oqpTyTTRjKM+7pxAJpcY9dgALugM+9H8qpRRAW9Ekro9+h/b0krjHDlRB91wXS8yeixJKKRVvdqirrPqxJnqgCnq0u01IdISulPJJbt1i3k/+Oinb5sc9dqAKuuMJP41eyo68Cr9TUUolKDskZEsbxumIe+xgFXRsHnIvoi7vJL9TUUolqFD3lK+nXS7HJupEKJVqUk2b36kopRKUFe5qW/T0xqJj4zZX83byvzGy+iW/U1FKJSjL7hqhG1dH6MfEjXZ/gN2N/UopFXdp+fzFmUZzSvyXIAlUQXe6u1xC2raolPJJKGsI/+5cy86sifGPHfeIfWj3RQixtaArpfxhW9196D7sKRqogu50X4QQnXJRSvkkub2WtclXULbhqbjHDlRB70gu4sfRK2nPG+t3KkqpBGXZYWzx9KLosepMzuV37nk42WV+p6KUSlC72xbxtKAfE7ejmbGymWSv3e9UlFIJKtxd0I3rxD12oAp6anUlLyXfTFbDSr9TUUolKHv3CN2N/41FgVo43HO72xa1y0Up5RPbDjPbOY+s9PFxjx2oEbrpblu0bO1yUUr5Q0Ih7vJmsi5ratxjB6ygd/2JowVdKeWnNCuKceK/t3GvCrqInC8iq0VkrYjcfJDjXxaRZd1f74jIibFPtWde90WIPVeZlVLKB/8KfZOzNz8Q97g9FnQRsYAHgQuA8cAMEdl/cmgDcLYx5gTgTmBWrBPtjdqsCXw/+k0kM/5rKCil1G6O2IjXP7tcTgHWGmPWG2MiwBzgor1PMMa8Y4zZ1f3wPSD+m+kBjanF/NU9Gystx4/wSikFgIuF9NM+9GJgy16Pq7qfO5SrgRcPdkBErhGRRSKyqLa2tvdZ9pLdWs1k+Yiwif9vRqWU2s2h/47Q5SDPmYOeKHIOXQX9hwc7boyZZYypMMZUFBYW9j7LXire/gpPJ99O2GmJ+WsrpVRvuWL5UtB704deBZTu9bgE2Lb/SSJyAvBb4AJjTF1s0jtC3X/i6EVRpZSf/hH+NMnppcR7d+PejNAXAqNEpFxEkoDLgGf3PkFEhgFPA18xxnwU+zR7Z/ettmEt6EopH/099WIWpp0d97g9jtCNMY6I3AC8DFjAY8aYFSJybffxh4HbgHzgIREBcIwx8f7ltOdWW1sLulLKR9m0kRR14x63V7f+G2NeAF7Y77mH9/r+68DXY5vaUeies7L11n+llI/uar2Njs4s4Ny4xg3UnaIrcz/G9dHvIKFAvS2l1ADjik3Ih267QC3OVZ1Szv+GDtaUo5RS8eP5VNADNZTNblnHGSFdOlcp5S9PLEJe/OfQA1XQK2r+xs/kF36noZRKcJ7YWOiUyzERL4qL5XcaSqkE907WBbS1NPO9OMcN1Agd18FBO1yUUv5aljWdl+xz4h43UCP0kIniiI7QB4JoNEpVVRUdHR1+pzKgpKSkUFJSQjisA5f+LMc0ku/Efr2qngSroHtRXAnUWwqsqqoqMjMzKSsro/tmNNUDYwx1dXVUVVVRXl7udzrqMD638zcUt1cCl8Y1bqCq39ycK2iknp/7nYjqUUdHhxbzIyQi5Ofn0xcrlarYMmJjax/6sdlkl1OTPMTvNFQvaTE/cvqZDQzGCmPRT2/9HyhGtFYy1IkCZ72lgMkAAAtISURBVPmdilIqkYmNrW2Lx+bixie67866zu9UlFIJzFhhbKM3Fh2TkHHw9KKo8sGuXbt6PkkljI/yz+Fu76txjxuo6hcyDlErxe801BG6Y+4KVm5riulrjh+axY8/c/whj2/cuJELL7yQDz74AICf/exntLS0cPvttzN9+nQmTZrEggULaGpq4rHHHuOUU045bLz77ruPV199lauvvpoZM2aQlZV1yHMff/xxFi1axAMPdO0Kf+GFF/L973+f6dOnk5GRwTe/+U1ef/11cnNzmTNnDn2xu5fqWzXZJ/EnJ5O74hw3UCN0yzgYHaGrGGhtbeWdd97hoYce4mtf+1qP599999088cQTrF+/nsmTJzNz5kzmzZt3VHEnT57MkiVLOPvss7njjjuOJn3lsyy3nnFswHO9uMYNVPWzjKtTLgPQ4UbSfpkxYwYA06ZNo6mpiYaGBnJycg77M2PGjOHee+/l7rvvZs6cOVx44YV89atf5Ve/+lWv44ZCIS69tKt3+YorruBzn/vc0b8J5ZsTap7lmuSHiESvJslKjVvcQFW/u1L+jdLCHE7yOxHV79m2jef93+hp/ztW928P3P/xVVddxdKlSxk6dCgvvNC194sxhtdff53Zs2czf/58brjhBr7+9QP3fekp9uHiqgEi1FVaHaeTJOJX0AM15bJGhrMrdbjfaagBYNCgQdTU1FBXV0dnZyfPPffcPsefeuopAObNm0d2djbZ2dn7HJ89ezaVlZV7ivmTTz7J2LFjefDBB5kxYwYffvghP/nJTygrKzsgdllZGZWVlXiex5YtW1iwYMGeY57n8de//hWAP/7xj5x55pmxfNsqXuyubTCj0Wh8w8Y1Wh+b3vkmhR0jQMfoqgfhcJjbbruNqVOnUl5eztixY/c5npuby+mnn77nomhPhg8fzttvv01RUVGP555xxhmUl5czceJEJkyYwOTJk/ccS09PZ8WKFUyZMoXs7Ow9v1jUABPqWmvHjXTGNWygCvqNzmzWN50JfMXvVNQAcNNNN3HTTTcd9NjnP/957rnnnl6/1pGMpEWEJ5988pDH77zzTu68885ev57qf8TqLuhOfEfogZpysXAxoqvQKaX8VVc4le9EriMSzoxr3ECN0G3jgBWot6R88MYbb/gWu6WlxbfYKnY6ssr4u3cm3wnF74IoBGyEbuNiQkl+p6GUSnBpTiNT5UPczua4xg1gQdcRulLKX0X1i3gq+U5k18a4xg1MQTfGcEHkHt4vvszvVJRSCS6kF0WPjeMZ1poSoim67oVSyl9i7y7okbjGDU5Bj0S42nqBwW2r/U5FDUC33347P/vZz3yJPXPmzD03E6lgCFld1/I8HaEfnWhnKz8K/4HSpiV+p6ISkC6fq/YW6h6he3EeoQfmCqIb7f7gQtqHPiDN/vSBzx1/MZzyDYi0wZNfPPD4pMvhpC9Dax38eb+1p696vseQd911F7///e8pLS2lsLCQKVOmADB9+nSmTp3K66+/TkNDA48++ihnnXX4XbCeeuopHnjgAWbOnMmVV1552CVvjTHceOONvPbaa5SXl2OM2XOsrKyMK6+8krlz5xKNRvnLX/5ywF2sqv+L5o/hG5HvclXW6LjGDcwIfXdB3z13pdThLF68mDlz5rB06VKefvppFi5cuM9xx3FYsGAB999/f6+WsL322mt58cUXaW9vZ9q0aXzhC1/gpZde2mcRrt2eeeYZVq9ezfLly3nkkUd455139jleUFDAkiVL+Na3vuXbNJA6NpKWzyteBe3h3LjGDcwI3XG61kzYfXVZDTCHG1EnpR3+eHp+r0bke3v77be55JJLSEtLA+Czn/3sPsd3L1s7ZcoUNm7c2KvXLC0t5Uc/+hG33norL730EldffTVTpkzh2Wef3ee8t956ixkzZmBZFkOHDuXcc889ZOynn376iN6X6h+S3FbOCS0l1FIKDIpb3F6N0EXkfBFZLSJrReTmgxwXEflV9/FlIjL5YK/Tl/ZMuWhBV710uKVpk5OTAbAsC8c5cLPfW265hUmTJjFp0qR9nl+wYAHXXXcdN954I1/84hcPuR7MscRW/V9q+3ZmJ91HVu3Cnk+OoR4LuohYwIPABcB4YIaIjN/vtAuAUd1f1wC/iXGePWpPL+a0jl9TU/KJeIdWA9C0adN45plnaG9vp7m5mblz5x7Rz991111UVlZSWVkJwD//+U9OOOEEbr31VqZPn87KlSu5//77Of74AzfvmDZtGnPmzMF1XbZv387rr78ek/ek+g+re+rXxLnLpTdTLqcAa40x6wFEZA5wEbByr3MuAn5vuq7uvCciOSIyxBizPdYJv/lRLev/9mPOib61z/OesdnOXYSSMmIdUgXQ5MmTufTSS5k0aRLDhw/v8aJnT/Lz85k7dy7Dh/e8Hv8ll1zCa6+9xsSJExk9ejRnn332McVW/Y9ld/2VNWzJvayr/A3XZnTtWvW1jt8z2Ktm3dm/4utnHRfzuL0p6MXAlr0eVwFTe3FOMbBPQReRa+gawTNs2LAjzRWAjGSbcPZg6tvK93nexeZzY4upKMs7qtdVieeWW27hlltuOeD5vRfnKigo6NUc+u4Omd4QkT0bRO9v71gVFRW+LhSmjt6g0pHML/gc4Y6duFiMGtQ10JSGoXQ6SRRkJPdJ3N4U9INN9pmjOAdjzCxgFkBFRcUBx3tjyvBcplx320GPnXw0L6iUUjFm2TZTb5i95/H/1abe/+I/Gr25KFoFlO71uATYdhTnKKWU6kO9KegLgVEiUi4iScBlwLP7nfMs8NXubpdTgca+mD9XwbL3DTWqd/QzU4fT45SLMcYRkRuAlwELeMwYs0JEru0+/jDwAvApYC3QBlzVdymrIEhJSaGuro78/Hzd2b6XjDHU1dWRkpLidyqqnxK/fuNXVFSYRYsW+RJb+S8ajVJVVUVHR4ffqQwoKSkplJSUEA7r/RaJSkQWG2MqDnYsMHeKqoElHA5TXl7e84lKqV4LzFouSimV6LSgK6VUQGhBV0qpgPDtoqiI1AKb+ujlC4CdffTaQaCfT8/0Mzo8/Xx61lef0XBjzEEX3PetoPclEVl0qKvASj+f3tDP6PD08+mZH5+RTrkopVRAaEFXSqmACGpBn+V3Av2cfj4908/o8PTz6VncP6NAzqErpVQiCuoIXSmlEo4WdKWUCohAFfSeNrNOdCLymIjUiMgHfufSH4lIqYi8LiIfisgKEfm23zn1NyKSIiILROT97s/oDr9z6o9ExBKRpSLyXDzjBqag93Iz60T3OHC+30n0Yw7wPWPMOOBU4Hr9b+gAncC5xpgTgUnA+d17IKh9fRv4MN5BA1PQ2Wsza2NMBNi9mbXqZox5C6j3O4/+yhiz3RizpPv7Zrr+hyz2N6v+xXRp6X4Y7v7Szoq9iEgJ8Gngt/GOHaSCfqiNqpU6YiJSBpwEzPc3k/6nezqhEqgBXjHG6Ge0r/uBHwBevAMHqaD3aqNqpXoiIhnA34DvGGOa/M6nvzHGuMaYSXTtHXyKiEzwO6f+QkQuBGqMMYv9iB+kgq4bVatjJiJhuor5k8aYp/3Opz8zxjQAb6DXZfZ2BvBZEdlI17TvuSLyh3gFD1JB781m1kodknRtbvoo8KEx5ud+59MfiUihiOR0f58KfBxY5W9W/Ycx5j+MMSXGmDK6atBrxpgr4hU/MAXdGOMAuzez/hD4szFmhb9Z9S8i8ifgXWCMiFSJyNV+59TPnAF8ha5RVWX316f8TqqfGQK8LiLL6BpEvWKMiWtrnjo0vfVfKaUCIjAjdKWUSnRa0JVSKiC0oCulVEBoQVdKqYDQgq6UUgGhBV0ppQJCC7pSSgXE/weNfJlrWc1utwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#plot_conductance(syst, energies=np.linspace(-3,3, 100))\n",
    "#plot_spin_conductance(syst, energies=np.linspace(0, 3, 30))\n",
    "plot_spin_conductance(syst, energies=np.linspace(-0.1,4.1, 100))"
   ]
  }
 ],
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}