A quick binder with a widget plot the moire peaks of two graphene lattices and an hBN lattice for different angles

requirements.txt

numpy
matplotlib
ipywidgets

three_moire_plot.ipynb

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       "interactive(children=(FloatSlider(value=1.9, continuous_update=False, description='theta_2', max=5.0, min=-5.0…"
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   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from ipywidgets import interactive\n",
    "import ipywidgets as widgets\n",
    "from itertools import combinations, permutations, product\n",
    "\n",
    "def colormix(c1, c2):\n",
    "    if 'red' in [c1,c2]:\n",
    "        if 'yellow' in [c1,c2]:\n",
    "            return 'orange'\n",
    "        elif 'green' in [c1,c2]:\n",
    "            return 'maroon'\n",
    "        elif 'purple':\n",
    "            return 'blue'\n",
    "    else:\n",
    "        return 'xkcd:lime'\n",
    "    \n",
    "def rotate(vec, angle):\n",
    "    R = np.array([[np.cos(angle), -np.sin(angle)], \n",
    "                  [np.sin(angle), np.cos(angle)]])\n",
    "    return R @ vec\n",
    "\n",
    "def plot_moire(theta_2, theta_hBN, ordertwo=True):\n",
    "    r_g = 1 / (0.5*np.sqrt(3)*0.246)\n",
    "    t1 = np.deg2rad(1)\n",
    "    k_g = r_g*np.array([np.cos(t1), np.sin(t1)]) \n",
    "    ks_g = np.stack([rotate(k_g, np.pi/3*i) for i in range(6)])\n",
    "    fig, ax = plt.subplots(figsize=[15,15])\n",
    "    t2 = np.deg2rad(theta_2)\n",
    "    k_g2 = r_g*np.array([np.cos(t1+t2), np.sin(t1+t2)]) \n",
    "    ks_g2 = np.stack([rotate(k_g2, np.pi/3*i) for i in range(6)])\n",
    "    r_hBN = 1 / (0.5*np.sqrt(3)*0.2504)\n",
    "    thBN = np.deg2rad(theta_hBN)\n",
    "    k_hBN = r_hBN*np.array([np.cos(t1+thBN), np.sin(t1+thBN)]) \n",
    "    ks_hBN = np.stack([rotate(k_hBN, np.pi/3*i) for i in range(6)])\n",
    "    ax.scatter(*ks_g.T, s=25, label='graphene 1', c='C0')\n",
    "    ax.scatter(*ks_g2.T, s=25, label='graphene 2', c='C1')\n",
    "    ax.scatter(*ks_hBN.T, s=25, label='hBN', c='C2')\n",
    "    vs = {'red': ks_g-ks_hBN,\n",
    "          'yellow': ks_g-ks_g2,\n",
    "          'green': ks_g2-ks_hBN\n",
    "         }\n",
    "    ax.scatter(*(vs['red']).T, s=75, \n",
    "               label=f'G1 - hBN ', \n",
    "               c='red', edgecolor='black')\n",
    "    ax.scatter(*(vs['yellow']).T, s=75, \n",
    "               label=f'G1 - G2 ', \n",
    "               c='yellow', edgecolor='black')\n",
    "    ax.scatter(*(vs['green']).T, s=75, \n",
    "               label=f'G2 - hBN', \n",
    "               c='green', edgecolor='black')\n",
    "    ax.scatter(0,0,c='C0', s=75)\n",
    "    if ordertwo:\n",
    "        for key, key2 in combinations(['yellow', 'green', 'red'], 2):\n",
    "            vdiffs = np.stack([k1 - k2 for k1,k2 in product(vs[key],vs[key2])])\n",
    "            plt.scatter(*vdiffs.T, color=colormix(key, key2), edgecolor='black', \n",
    "                        alpha=0.3, s=300, label=key+'-'+key2)\n",
    "    ax.set_aspect('equal')\n",
    "    plt.gca().set_xlim([-0.28,0.28])\n",
    "    plt.gca().set_ylim([-0.28,0.28])\n",
    "    plt.legend()\n",
    "    \n",
    "interactive(plot_moire, \n",
    "        theta_2=widgets.FloatSlider(value=1.9, min=-5, max=5,step=0.05, continuous_update=False),\n",
    "        theta_hBN=widgets.FloatSlider(value=0.9, min=-5, max=5,step=0.05, continuous_update=False)\n",
    "       )"
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