chern_number.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from tb_hamiltonian.continuum import GrapheneContinuumModel\n",
    "\n",
    "inputs = dict(\n",
    "    bond_length=1.425,\n",
    "    interlayer_hopping=0.22,\n",
    "    superlattice_potential_periodicity=500,\n",
    "    superlattice_potential_amplitude=0.020,\n",
    "    gate_bias=0.024,\n",
    "    layer_potential_ratio=0.3,\n",
    "    nearest_neighbor_order=1,\n",
    ")\n",
    "\n",
    "model = GrapheneContinuumModel(**inputs)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "from tb_hamiltonian.continuum import interpolate_path\n",
    "from tb_hamiltonian.utils import BandStructure\n",
    "from tb_hamiltonian.continuum import compute_eigenstuff\n",
    "\n",
    "# Generate high-symmetry points in the mini Brillouin zone (BZ)\n",
    "b1, b2 = model.Qn[0], model.Qn[1]\n",
    "\n",
    "high_sym_points = {\n",
    "    \"Γ\": np.array([0.0, 0.0]),\n",
    "    \"M\": b1 / 2,\n",
    "    \"K\": (b1 + b2) / 3,\n",
    "}\n",
    "\n",
    "Gamma = np.array([0.0, 0.0])\n",
    "M = b1 / 2\n",
    "K = (b1 + b2) / 3\n",
    "\n",
    "path = \"Γ K M Γ\"\n",
    "path_points = [high_sym_points[k] for k in path.split()]\n",
    "kpath, k_point_indices = interpolate_path(path_points, total_points=100)\n",
    "eigenvalues, eigenvectors = compute_eigenstuff(model.H_total_K, kpath)\n",
    "\n",
    "nbands = eigenvalues.shape[1]\n",
    "mid_band = int(nbands / 2)\n",
    "EF = (np.min(eigenvalues[:, mid_band]) + np.max(eigenvalues[:, mid_band - 1])) / 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "bs = BandStructure(\n",
    "    high_sym_points=high_sym_points,\n",
    "    path=path,\n",
    "    distances=[*range(len(eigenvalues))],\n",
    "    eigenvalues=eigenvalues,\n",
    "    high_sym_indices=k_point_indices,\n",
    "    e_fermi=EF,\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<Axes: title={'center': 'Band Structure'}, ylabel='Energy (eV)'>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "bs.plot(fig_params={\"ylim\": (-0.04, 0.04)}, plot_params={\"color\": \"black\"})"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Chern number: 0.013831020675402263\n",
      "Chern number log: -0.00012125311968689299\n"
     ]
    }
   ],
   "source": [
    "def compute_berry_curvature(kx, ky, dkx, dky, bnd_idx, H_calculator):\n",
    "    # Get the wavefunction/eigenvectors (assuming we are interested in band number bnd_idx)\n",
    "    _, psi = compute_eigenstuff(H_calculator, [[kx, ky]])\n",
    "    _, psi_dkx = compute_eigenstuff(H_calculator, [[kx + dkx, ky]])\n",
    "    _, psi_dky = compute_eigenstuff(H_calculator, [[kx, ky + dky]])\n",
    "\n",
    "    # Finite differences to approximate derivatives\n",
    "    dpsi_dkx = (psi[0, :, bnd_idx] - psi_dkx[0, :, bnd_idx]) / dkx\n",
    "    dpsi_dky = (psi[0, :, bnd_idx] - psi_dky[0, :, bnd_idx]) / dky\n",
    "\n",
    "    return np.imag(np.vdot(dpsi_dkx, dpsi_dky) - np.vdot(dpsi_dky, dpsi_dkx))\n",
    "\n",
    "\n",
    "# Function to compute Berry curvature using the logarithmic approach\n",
    "def compute_berry_curvature_log(kx, ky, dkx, dky, bnd_idx, H_calculator):\n",
    "    _, psi = compute_eigenstuff(H_calculator, [[kx, ky]])\n",
    "    _, psi_right = compute_eigenstuff(H_calculator, [[kx + dkx, ky]])\n",
    "    _, psi_up = compute_eigenstuff(H_calculator, [[kx, ky + dky]])\n",
    "    _, psi_diag = compute_eigenstuff(H_calculator, [[kx + dkx, ky + dky]])\n",
    "\n",
    "    psi = psi[0, :, bnd_idx]\n",
    "    psi_right = psi_right[0, :, bnd_idx]\n",
    "    psi_up = psi_up[0, :, bnd_idx]\n",
    "    psi_diag = psi_diag[0, :, bnd_idx]\n",
    "\n",
    "    # Overlaps (link variables)\n",
    "    Ux = np.vdot(psi, psi_right)\n",
    "    Uy = np.vdot(psi, psi_up)\n",
    "    Ux_dagger = np.vdot(psi_up, psi_diag)\n",
    "    Uy_dagger = np.vdot(psi_right, psi_diag)\n",
    "\n",
    "    return np.imag(np.log(Ux * Uy * np.conj(Ux_dagger) * np.conj(Uy_dagger)))\n",
    "\n",
    "\n",
    "# Compute Chern number by integrating Berry curvature over the Brillouin zone\n",
    "def compute_chern_number(kx_vals, ky_vals, dkx, dky, bnd_idx, H_calculator):\n",
    "    berry_flux = 0\n",
    "    berry_flux_log = 0\n",
    "    for kx in kx_vals:\n",
    "        for ky in ky_vals:\n",
    "            berry_flux += compute_berry_curvature(\n",
    "                kx, ky, dkx, dky, bnd_idx, H_calculator\n",
    "            )\n",
    "            berry_flux_log += compute_berry_curvature_log(\n",
    "                kx, ky, dkx, dky, bnd_idx, H_calculator\n",
    "            )\n",
    "    # Normalization by BZ area\n",
    "    chern_number = berry_flux * dkx * dky / (2 * np.pi)\n",
    "    chern_number_log = berry_flux_log * dkx * dky / (2 * np.pi)\n",
    "    return chern_number, chern_number_log\n",
    "\n",
    "\n",
    "# Constants for Brillouin zone grid\n",
    "nkpts = 20  # Number of grid points along each direction\n",
    "\n",
    "kx_vals = np.linspace(-np.pi, np.pi, nkpts)\n",
    "ky_vals = np.linspace(-np.pi, np.pi, nkpts)\n",
    "\n",
    "dkx = kx_vals[1] - kx_vals[0]\n",
    "dky = ky_vals[1] - ky_vals[0]\n",
    "\n",
    "H_calculator = model.H_total_K\n",
    "\n",
    "bnd_idx = mid_band\n",
    "chern, chern_log = compute_chern_number(\n",
    "    kx_vals, ky_vals, dkx, dky, bnd_idx, H_calculator\n",
    ")\n",
    "print(f\"Chern number: {chern}\")\n",
    "print(f\"Chern number log: {chern_log}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "tbh",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.14"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}