FitDiracParabolic.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Fitting Dirac band with parabolic band"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "from numpy import frompyfunc, linspace, exp, log, pi, zeros, arange\n",
    "from mpmath import polylog\n",
    "from scipy.integrate import quad\n",
    "from matplotlib.ticker import AutoMinorLocator\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "\n",
    "SMALL_SIZE = 14\n",
    "MEDIUM_SIZE = 16\n",
    "BIGGER_SIZE = 18\n",
    "\n",
    "plt.rc('font', size =SMALL_SIZE)\n",
    "plt.rc('legend', fontsize = SMALL_SIZE)\n",
    "plt.rc('xtick', labelsize = MEDIUM_SIZE)\n",
    "plt.rc('ytick', labelsize = MEDIUM_SIZE)\n",
    "plt.rc('axes', labelsize = BIGGER_SIZE)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Specific treatment for polylogarithm function\n",
    "\n",
    "plog = frompyfunc(polylog, 2,1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Tune Band Gap"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "delta = 6"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Dirac Band "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "infinity = 100  # this value is sufficient for our function\n",
    "\n",
    "\n",
    "# Define Kernel:\n",
    "\n",
    "## conduction band\n",
    "def F0c(x):\n",
    "    return exp(x)/(1+exp(x))\n",
    "def F1c(x):\n",
    "    return ( x/(1+exp(x)) + log(1+exp(-x)) )\n",
    "def F2c(x):\n",
    "    return ( (pi**2)/3 - (x**2 / (1+exp(x)) )\n",
    "            - 2*x*log(1+exp(-x)) + 2*plog(2,-exp(-x)) )\n",
    "def F3c(x):\n",
    "    return ( (x**3)/(1+exp(x)) + 3*(x**2)*log(1+exp(-x)) - 6*x*plog(2,-exp(-x)) - 6*plog(3,-exp(-x)) )\n",
    "\n",
    "def G0c(xx,D):\n",
    "    def integrand(x, xx):\n",
    "        return (1 / (x + xx)) * (exp(x) / (exp(x)+1)**2)\n",
    "    I, error = quad(integrand, D, infinity, args=(xx))\n",
    "    return I\n",
    "def G1c(xx,D):\n",
    "    def integrand(x, xx):\n",
    "        return (x / (x + xx)) * (exp(x) / (exp(x)+1)**2)\n",
    "    I, error = quad(integrand, D, infinity, args=(xx))\n",
    "    return I\n",
    "def G2c(xx,D):\n",
    "    def integrand(x, xx):\n",
    "        return (x**2 / (x + xx)) * (exp(x) / (exp(x)+1)**2)\n",
    "    I, error = quad(integrand, D, infinity, args=(xx))\n",
    "    return I\n",
    "\n",
    "## valence band\n",
    "def F0v(x):\n",
    "    return 1/(1+exp(x))\n",
    "def F1v(x):\n",
    "    return ( -x/(1+exp(x)) - log(1+exp(-x)) )\n",
    "def F2v(x):\n",
    "    return ( (x**2 / (1+exp(x)) ) + 2*x*log(1+exp(-x))\n",
    "            - 2*plog(2,-exp(-x)) )\n",
    "def F3v(x):\n",
    "    return ( -(x**3)/(1+exp(x)) - 3*(x**2)*log(1+exp(-x)) + 6*x*plog(2,-exp(-x)) + 6*plog(3,-exp(-x)) )\n",
    "\n",
    "def G0v(xx,D):\n",
    "    def integrand(x, xx):\n",
    "        return (1 / (x + xx)) * (exp(x) / (exp(x)+1)**2)\n",
    "    I, error = quad(integrand, -infinity, -D, args=(xx))\n",
    "    return I\n",
    "def G1v(xx,D):\n",
    "    def integrand(x, xx):\n",
    "        return (x / (x + xx)) * (exp(x) / (exp(x)+1)**2)\n",
    "    I, error = quad(integrand, -infinity, -D, args=(xx))\n",
    "    return I\n",
    "def G2v(xx,D):\n",
    "    def integrand(x, xx):\n",
    "        return (x**2 / (x + xx)) * (exp(x) / (exp(x)+1)**2)\n",
    "    I, error = quad(integrand, -infinity, -D, args=(xx))\n",
    "    return I\n",
    "\n",
    "# ZT function:\n",
    "def ZT(Seeb,Sig,KappaE,KappaP):\n",
    "    return (Seeb**2 * Sigma)/(KappaE + KappaP)\n",
    "\n",
    "# Create sample points within [-10,10]:\n",
    "npoint  = 101\n",
    "eta     = linspace(-10, 10, npoint) \n",
    "\n",
    "L0c     = zeros(npoint,float)\n",
    "L1c     = zeros(npoint,float)\n",
    "L2c     = zeros(npoint,float)\n",
    "\n",
    "L0v     = zeros(npoint,float)\n",
    "L1v     = zeros(npoint,float)\n",
    "L2v     = zeros(npoint,float)\n",
    "\n",
    "S_c     = zeros(npoint,float)\n",
    "Sigma_c = zeros(npoint,float)\n",
    "kappa_c = zeros(npoint,float)\n",
    "\n",
    "S_v     = zeros(npoint,float)\n",
    "Sigma_v = zeros(npoint,float)\n",
    "kappa_v = zeros(npoint,float)\n",
    "\n",
    "S       = zeros(npoint,float)\n",
    "Sigma   = zeros(npoint,float)\n",
    "kappae  = zeros(npoint,float)\n",
    "\n",
    "for i in range(eta.size):\n",
    "    L0c[i] = F1c(eta[i] - delta) + eta[i] * F0c(eta[i] - delta) - delta**2 * G0c(eta[i],delta-eta[i])\n",
    "    L1c[i] = F2c(eta[i] - delta) + eta[i] * F1c(eta[i] - delta) - delta**2 * G1c(eta[i],delta-eta[i])\n",
    "    L2c[i] = F3c(eta[i] - delta) + eta[i] * F2c(eta[i] - delta) - delta**2 * G2c(eta[i],delta-eta[i])\n",
    "    L0v[i] = -1 * (F1v(eta[i] + delta) + eta[i] * F0v(eta[i] + delta) - delta**2 * G0v(eta[i],delta+eta[i]))\n",
    "    L1v[i] = -1 * (F2v(eta[i] + delta) + eta[i] * F1v(eta[i] + delta) - delta**2 * G1v(eta[i],delta+eta[i]))\n",
    "    L2v[i] = -1 * (F3v(eta[i] + delta) + eta[i] * F2v(eta[i] + delta) - delta**2 * G2v(eta[i],delta+eta[i]))   \n",
    "    \n",
    "# TE quantities:\n",
    "S_c     = -L1c / L0c\n",
    "S_v     = -L1v / L0v\n",
    "Sigma_c =  L0c\n",
    "Sigma_v =  L0v\n",
    "Kappa_c =  L2c - (L1c**2 / L0c)\n",
    "Kappa_v =  L2v - (L1v**2 / L0v)\n",
    "\n",
    "Sigma   =  Sigma_c + Sigma_v\n",
    "S       = (Sigma_c * S_c + Sigma_v * S_v) / Sigma\n",
    "Kappae  = ( (Kappa_c + Kappa_v)\n",
    "          + (Sigma_c * Sigma_v)*(S_c - S_v)**2 / (Sigma) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Parabolic Band "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Define kernel:\n",
    "## conduction band\n",
    "def F0cc(xx):\n",
    "    return exp(xx)/(1+exp(xx))\n",
    "def F1cc(xx):\n",
    "    return ( xx/(1+exp(xx)) + log(1+exp(-xx)) )\n",
    "def F2cc(xx):\n",
    "    return ( (pi**2)/3 - (xx**2 / (1+exp(xx)) )\n",
    "            - 2*xx*log(1+exp(-xx)) + 2*plog(2,-exp(-xx)) )\n",
    "def F3cc(xx):\n",
    "    return ( (xx**3)/(1+exp(xx)) + 3*(xx**2)*log(1+exp(-xx)) - 6*xx*plog(2,-exp(-xx)) - 6*plog(3,-exp(-xx)) )\n",
    "\n",
    "## valence band\n",
    "def F0vv(xx):\n",
    "    return -1/(1+exp(xx))\n",
    "def F1vv(xx):\n",
    "    return ( xx/(1+exp(xx)) + log(1+exp(-xx)) )\n",
    "def F2vv(xx):\n",
    "    return -( (xx**2 / (1+exp(xx)) ) + 2*xx*log(1+exp(-xx))\n",
    "            - 2*plog(2,-exp(-xx)) )\n",
    "def F3vv(xx):\n",
    "    return ( (xx**3)/(1+exp(xx)) + 3*(xx**2)*log(1+exp(-xx)) - 6*xx*plog(2,-exp(-xx)) - 6*plog(3,-exp(-xx)) )\n",
    "\n",
    "# ZT function:\n",
    "def ZT1(Seeb,Sig,KappaE,KappaP):\n",
    "    return (Seeb**2 * Sig)/(KappaE + KappaP)\n",
    "\n",
    "# Create sample points within [-10,10]:\n",
    "npoint  = 101\n",
    "eta     = linspace(-10, 10, npoint) \n",
    "\n",
    "# TE quantities:\n",
    "etac= eta-delta\n",
    "etav= eta+delta\n",
    "\n",
    "L0cc = 2*F1cc(etac) + ((etac)*2*F0cc(etac))\n",
    "L1cc = 2*F2cc(etac) + ((etac)*2*F1cc(etac))\n",
    "L2cc = 2*F3cc(etac) + ((etac)*2*F2cc(etac))\n",
    "\n",
    "L0vv = 2*F1vv(etav)+(etav*2*F0vv(etav))\n",
    "L1vv = 2*F2vv(etav)+(etav*2*F1vv(etav))\n",
    "L2vv = 2*F3vv(etav)+(etav*2*F2vv(etav))\n",
    "\n",
    "S_cc     = -L1cc / L0cc\n",
    "Sigma_cc = L0cc\n",
    "kappa_cc = L2cc - (L1cc**2 / L0cc)\n",
    "\n",
    "S_vv     = -L1vv/L0vv\n",
    "Sigma_vv = L0vv\n",
    "kappa_vv = L2vv - (L1vv**2/L0vv)\n",
    "\n",
    "Sigma1   = Sigma_cc + Sigma_vv\n",
    "S1       = (Sigma_cc * S_cc + Sigma_vv * S_vv) / Sigma1\n",
    "Kappae1  = ( (kappa_cc + kappa_vv)\n",
    "          + (Sigma_cc * Sigma_vv)*(S_cc - S_vv)**2 / (Sigma1) )\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Plotting "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 4 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Define the size of the entire plot\n",
    "plt.figure(figsize=(6,4))\n",
    "\n",
    "#Blue line for Dirac Band\n",
    "#Red Line for Parabolic Band\n",
    "\n",
    "# Subplot (a): Seebeck's coefficient\n",
    "ax1 = plt.subplot(2,2,1)\n",
    "plt.plot(eta, S, color='royalblue', linestyle='--', lw=2)\n",
    "plt.plot(eta, S1, color='purple', linestyle='-', lw=2)\n",
    "plt.ylabel('$S$ $(S_0)$')\n",
    "plt.axis([-10,10,-8,8]) # the format is [xmin,xmax,ymin,ymax]\n",
    "plt.xticks(range(-10,11,5))\n",
    "ax1.xaxis.set_minor_locator(AutoMinorLocator(5))\n",
    "plt.yticks(range(-8,9,4))\n",
    "ax1.yaxis.set_minor_locator(AutoMinorLocator(4))\n",
    "ax1.yaxis.labelpad = -4\n",
    "plt.text(4.5,4.7, r'$\\tilde{\\Delta} = 6$', fontsize=14)\n",
    "plt.text(-16,7.2,'(a)',fontsize=16)\n",
    "\n",
    "# Subplot (b): Electrical conductivity\n",
    "ax2 = plt.subplot(2,2,2)\n",
    "plt.plot(eta, Sigma, color='royalblue', linestyle='--', lw=2)\n",
    "plt.plot(eta, Sigma1, color='purple', linestyle='-', lw=2)\n",
    "plt.ylabel('$\\sigma$ $(\\sigma_0)$')\n",
    "plt.axis([-10,10,0,6]) # the format is [xmin,xmax,ymin,ymax]\n",
    "plt.xticks(range(-10,11,5))\n",
    "ax2.xaxis.set_minor_locator(AutoMinorLocator(5))\n",
    "plt.yticks(arange(0,7,step=2))\n",
    "ax2.yaxis.set_minor_locator(AutoMinorLocator(5))\n",
    "plt.text(-15.5,5.7,'(b)',fontsize=16)\n",
    "plt.text(0, 1.0, 'Dirac', color='royalblue', fontsize=14)\n",
    "plt.text(0, 5, 'Parabolic', color='purple', fontsize=14)\n",
    "\n",
    "\n",
    "# Subplot (c): Thermal conductivity (electron part)\n",
    "ax3 = plt.subplot(2,2,3)\n",
    "plt.plot(eta, Kappae, color='royalblue', linestyle='--', lw=2)\n",
    "plt.plot(eta, Kappae1, color='purple', linestyle='-', lw=2)\n",
    "plt.xlabel('$\\mu$ $(k_B T)$')\n",
    "plt.ylabel('$\\kappa_e$ $(\\kappa_0)$')\n",
    "plt.axis([-10,10,0,12]) # the format is [xmin,xmax,ymin,ymax]\n",
    "plt.xticks(range(-10,11,5))\n",
    "ax3.xaxis.set_minor_locator(AutoMinorLocator(5))\n",
    "plt.yticks(range(0,17,4))\n",
    "ax3.yaxis.set_minor_locator(AutoMinorLocator(4))\n",
    "plt.text(-16.5,15,'(c)',fontsize=16)\n",
    "\n",
    "# Subplot (d): ZT\n",
    "ax4 = plt.subplot(2,2,4)\n",
    "plt.plot(eta, ZT(S, Sigma, Kappae, 1), color='crimson', linestyle='--', lw=2)\n",
    "plt.plot(eta, ZT(S1, Sigma1, Kappae1, 1), color='crimson', linestyle='-', lw=2)\n",
    "plt.plot(eta, ZT(S, Sigma, Kappae, 5), color='darkgreen', linestyle='--', lw=2)\n",
    "plt.plot(eta, ZT(S1, Sigma1, Kappae1, 5), color='darkgreen', linestyle='-', lw=2)\n",
    "plt.xlabel('$\\mu (k_B T)$')\n",
    "plt.ylabel('$ZT$')\n",
    "plt.axis([-10,10,0,4]) # the format is [xmin,xmax,ymin,ymax]\n",
    "plt.xticks(range(-10,11,5))\n",
    "ax4.xaxis.set_minor_locator(AutoMinorLocator(5))\n",
    "plt.yticks(arange(0,4.1,step=1))\n",
    "ax4.yaxis.set_minor_locator(AutoMinorLocator(4))\n",
    "plt.text(4.5,3.5, r'$r_\\kappa = 1$', fontsize=12, color='crimson')\n",
    "plt.text(4.5, 3, r'$r_\\kappa = 5$', fontsize=12, color='darkgreen')\n",
    "plt.text(-15.5,3.75,'(d)',fontsize=16)\n",
    "\n",
    "# Save Figure\n",
    "plt.tight_layout(pad=0.1, w_pad=0.5, h_pad=0.1)\n",
    "plt.savefig('paraFigFitDirac.pdf')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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