{ "cells": [ { "cell_type": "markdown", "id": "b16c67c1", "metadata": {}, "source": [ "# Intro\n", "The BCS theory describes the system as a gas of quasiparticles of energies $E_{k}$. Quasiparticles are superpositions of particles and holes, such that $|v_{k}|^2$ is the probability of a particle with wave-vector $k$ and $|u_{k}|^2$ is the probability of a hole .\n", "The equation that describes a uniform gas of electrons in a superconducting/superfluid state has the following form (so-called BCS equations):\n", "\\begin{equation}\n", "\\left( \\begin{array}{cc}\n", "\\eta_{k} & \\Delta \\\\\n", "\\Delta^\\ast & -\\eta_{k} \\end{array} \\right) \\left( \\begin{array}{c} u_{k} \\\\ v_{k} \\end{array} \\right)\n", "=E_{k} \\left( \\begin{array}{c} u_{k} \\\\ v_{k} \\end{array} \\right) \\;,\n", "\\label{BdGnonuniform}\n", "\\end{equation}\n", "where $\\eta_{k}={\\frac{\\hbar^2k^{2}}{2m}}-\\mu$ is the energy of a free particle calculated with respect to the chemical potential $\\mu$. The relation must be satisfied:\n", "\\begin{equation}\n", "|v_{k}|^2 + |u_{k}|^2 =1,\\label{eq:norm}\n", "\\end{equation}\n", "which means that each state is occupied by one quasiparticle (also known as the Pauli principle). We can compute the number of particles in the system as:\n", "\\begin{equation}\n", "N=2\\sum_{k}|v_{k}|^2 f(-E_{k}),\\label{eq:n}\n", "\\end{equation}\n", "where the factor $2$ accounts for two spin projections ($\\uparrow$ and $\\downarrow$). The density of atoms is $n=N/V$, where $V$ is the volume of our system. The particles are distributed according to the Fermi-Dirac statistics:\n", "\\begin{equation}\n", "f(E_{k}) = \\frac{1}{e^{E_{k}/k_B T} +1}\n", "\\end{equation}\n", "where $T$ is temperature and $k_B$ is the Boltzmann constant. \n", "\n", "The most important quantity in the BCS theory is the energy gap (also known as \"gap parameter\") $\\Delta$. If $\\Delta>0$ then the system is in the superconducting state. It can be shown that this condition is equivalent to the appearance of Cooper pairs in the system: a quantum correlation between particles in states $(k,\\uparrow)$ and $(-k,\\downarrow)$, so that the energy required to break the pair is $E_{\\textrm{breaking}}= \\Delta$. Such correlated states can propagate in the system without energy losses (scatterings). If $\\Delta=0$, then the system is in the normal state. The energy gap is computed as follows:\n", "\n", "\\begin{equation}\n", "\\Delta = \\frac{g}{2V}\\sum_{k} u_{k}v_{k}(1-2f(E_{k})).\n", "\\end{equation}\n", "The coupling constant is related to the scattering lenght\n", "\\begin{equation}\n", "\\frac{1}{g}=-\\frac{m}{4\\pi\\hbar^2 a}+\\frac{k_c m}{2\\pi^2\\hbar^2}-\\frac{k_F m}{4\\pi^2\\hbar^2}\\ln\\left(\\frac{k_c+k_F}{k_c-k_F}\\right)\n", "\\end{equation}" ] }, { "cell_type": "markdown", "id": "82548ccd", "metadata": {}, "source": [ "# Solutions of BCS equations\n", "\n", "Let us define:\n", "\\begin{equation}\n", "E_{k}=\\sqrt{\\eta_{k}^2 + \\Delta^2},\\label{eq:Ek}\n", "\\end{equation}\n", "and \n", "\\begin{equation}\n", "A_{k}=\\frac{1}{2}\\left(1+\\frac{\\eta_{k}}{E_{k}}\\right)\n", "\\end{equation}\n", "It can be shown that the two solutions are:\n", "1. For a positive eigenvalue $E^{(+)}_{k}=+E_{k}$, the corresponding eigenvector obeys\n", "\\begin{equation}\n", "u_{k}^{(+)}=\\sqrt{A_{k}}\\;; \\;\\;\\;\\;\\; \n", "v_{k}^{(+)}=\\sqrt{1-A_{k}} \\;.\\label{eq:E1}\n", "\\end{equation}\n", "2. For a negative eigenvalue $E^{(-)}_{k}=-E_{k}$, the corresponding eigenvector obeys\n", "\\begin{equation}\n", "u_{k}^{(-)}=\\sqrt{1-A_{k}}\\;; \\;\\;\\;\\;\\; \n", "v_{k}^{(-)}=-\\sqrt{A_{k}} \\;.\\label{eq:E2}\n", "\\end{equation}\n", "\n", "\n", "By recalling that $\\eta_{k}={\\frac{\\hbar^2k^{2}}{2m}}-\\mu$, we recognize that a positive value of quasiparticle energy corresponds to a state above the Fermi surface, while negative indicates the state below the Fermi surface. (For zero temperature Fermi energy equals the chemical potential, $\\varepsilon_F(T=0)= \\mu$.)\n", "Note that the solutions depend on $\\Delta$, which in turn depends on the solutions $\\{u_k,v_k\\}$. On top of this, we look for a solution that represents a gas of a given density $n_0$. Thus we search for $\\Delta$ (energy gap) and $\\mu$ (chemical potential) so that all the above equations are satisfied. " ] }, { "cell_type": "markdown", "id": "873b3ca7", "metadata": {}, "source": [ "# Self-consitent solution\n", "\n", "To find the solution of BCS equations, set initial values for $\\Delta$ and $\\mu$ and follow the protocol:\n", "1. Solve BCS equations: find all $\\{u_k,v_k\\}$ and $E_k$.\n", "2. Compute the corresponding density $n=N/V$ and corresponding $\\Delta$. The value of the $\\Delta$ that you obtain in this step will be referred to as $\\Delta_{new}$.\n", "3. Check the difference between $\\Delta$ and $\\Delta_{new}$, and between $n_0$ and $n=N/V$. If $|\\Delta-\\Delta_{new}|<\\varepsilon_\\Delta$, and $|n_0-n|<\\varepsilon_n$, where $\\varepsilon_{\\Delta/n}$ is the tolerance (algorithm parameter) then we have convergence, and we can stop the algorithm.\n", "4. Update the chemical potential according to the prescription: \n", "\\begin{equation}\n", "\\label{eq:chempot}\n", "\\mu \\leftarrow \\mu+\\alpha_\\mu(n_0-n),\n", "\\end{equation}\n", "where $\\alpha_\\mu$ is the algorithm parameter.\n", "5. Update the $\\Delta$ according mixing prescription\n", "\\begin{equation}\n", "\\Delta\\leftarrow \\beta_\\Delta\\Delta_{new} + (1-\\beta_\\Delta)\\Delta,\n", "\\end{equation}\n", "where $\\beta_\\Delta$ is the algorithm parameter (typically $\\beta_\\Delta \\approx 0.5$ provides the best performance), and go back to step 1.\n" ] }, { "cell_type": "markdown", "id": "19248109", "metadata": {}, "source": [ "# Simple BCS code" ] }, { "cell_type": "code", "execution_count": 1, "id": "2c770517", "metadata": {}, "outputs": [], "source": [ "# imports\n", "import numpy as np\n", "import matplotlib.pyplot as plt" ] }, { "cell_type": "code", "execution_count": 2, "id": "258cadc8", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Number of states with kkc**2: # skip if momentum is above the cut-off scale \n", " continue\n", " \n", " k2v.append(k2)\n", "k2v=np.array(k2v)\n", "\n", "print(\"Number of states with k50.0: r[i]=0.0\n", " elif x[i]<-50.0: r[i]=1.0\n", " else: r[i]=1.0/(np.exp(x[i])+1.0)\n", " return r" ] }, { "cell_type": "code", "execution_count": 4, "id": "d2383c13", "metadata": {}, "outputs": [], "source": [ "# simple extra functions\n", "def kF(n):\n", " return (3.*np.pi**2*n)**(1./3.)\n", "def eF(n):\n", " return hbar**2*kF(n)**2/(2.*m)" ] }, { "cell_type": "code", "execution_count": 5, "id": "85798841", "metadata": {}, "outputs": [], "source": [ "# solver of bcs equations\n", "def solve_bcs(delta, mu, a_s, n0, T, alpha=0.5, beta=0.5, epsd=1.0e-6, epsn=1.0e-6, maxiters=10000):\n", " if T<1.0e-8: T=1.0e-8 # to avoid division by zero in Fermi-Dirac function\n", " \n", " # coupling constant - in medium regularized\n", " ginv=-1.*m/(4.*np.pi*hbar**2*a_s)+ m*kc/(2.*np.pi**2*hbar**2)- m*kF(n0)/(4.*np.pi**2*hbar**2)*np.log((kc+kF(n0))/(kc-kF(n0)))\n", " g=1.0/ginv\n", "\n", " \n", " for it in range(maxiters):\n", " etak=hbar**2*k2v/(2.*m)-mu\n", " Ek=np.sqrt(etak**2 + delta**2)\n", " Ak=0.5*(1.0+etak/Ek)\n", "\n", " # Step 1: solve BCS equations\n", " ## solutions with positive energies\n", " Ekp = Ek\n", " ukp=np.sqrt(Ak)\n", " vkp=np.sqrt(1.0-Ak)\n", " ## solutions with negative energies\n", " Ekm = -1.0*Ek\n", " ukm=np.sqrt(1.0-Ak)\n", " vkm=-1.0*np.sqrt(Ak)\n", "\n", " # Step 2: compute density and delta \n", " N= 2.0*np.sum(vkp**2*fFD(-1.0*Ekp,T)) # contributions from positive energy solutions\n", " N+=2.0*np.sum(vkm**2*fFD(-1.0*Ekm,T)) # contributions from negative energy solutions\n", " n=N/V\n", "\n", " delta_new= (g/V/2)*np.sum(ukp*vkp*(1.-2.*fFD(Ekp,T))) # contributions from positive energy solutions\n", " delta_new+=(g/V/2)*np.sum(ukm*vkm*(1.-2.*fFD(Ekm,T))) # contributions from positive energy solutions\n", " \n", " # Step 3: check convergence\n", " d_delta=np.abs(delta_new-delta)\n", " d_n=np.abs(n0-n)\n", " print(\"[%8d] delta=%10.6f; n=%10.6f; d_delta=%10.6g; d_n=%10.6g\" % (it, delta_new, n, d_delta, d_n), end='\\r')\n", " if d_delta" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot results \n", "akF=np.array(akF)\n", "delta_formula=8.0/np.exp(1.0)**2 * np.exp(np.pi / (2.0*akF))\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(1.0/akF, np.array(delta_per_eF), label=\"numerics\")\n", "ax.plot(1.0/akF, delta_formula, label=\"formula\")\n", "ax.set(xlabel=r'$ak_F$', ylabel=r'$\\Delta/\\varepsilon_F$')\n", "ax.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cd60022f", "metadata": {}, "source": [ "# Delta vs temperature" ] }, { "cell_type": "code", "execution_count": 8, "id": "6c270d95", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CONVERGED! delta= 0.094110; n= 0.030519; d_delta=7.61682e-07; d_n=9.8579e-07\n", "CONVERGED! delta= 0.094111; n= 0.030519; d_delta=6.1535e-07; d_n= 0\n", "CONVERGED! delta= 0.094111; n= 0.030519; d_delta=6.15375e-07; d_n=6.47097e-13\n", "CONVERGED! delta= 0.094111; n= 0.030519; d_delta=6.38507e-07; d_n=6.26962e-10\n", "CONVERGED! delta= 0.094108; n= 0.030519; d_delta=9.80783e-07; d_n=3.74842e-08\n", "CONVERGED! delta= 0.094083; n= 0.030518; d_delta=8.94902e-07; d_n=4.33697e-07\n", "CONVERGED! delta= 0.093991; n= 0.030517; d_delta=4.97666e-07; d_n=9.75831e-07\n", "CONVERGED! delta= 0.093777; n= 0.030516; d_delta=2.36542e-07; d_n=9.83506e-07\n", "CONVERGED! delta= 0.093382; n= 0.030515; d_delta=4.41786e-07; d_n=9.66102e-07\n", "CONVERGED! delta= 0.092749; n= 0.030514; d_delta=5.45047e-07; d_n=9.52223e-07\n", "CONVERGED! delta= 0.091827; n= 0.030513; d_delta=6.21713e-07; d_n=9.46118e-07\n", "CONVERGED! delta= 0.090572; n= 0.030512; d_delta=7.17712e-07; d_n=9.87966e-07\n", "CONVERGED! delta= 0.088944; n= 0.030511; d_delta=7.98633e-07; d_n=9.91038e-07\n", "CONVERGED! delta= 0.086899; n= 0.030510; d_delta=8.71573e-07; d_n=9.7468e-07\n", "CONVERGED! delta= 0.084392; n= 0.030509; d_delta=9.41562e-07; d_n=9.59452e-07\n", "CONVERGED! delta= 0.081367; n= 0.030508; d_delta=9.70042e-07; d_n=9.10047e-07\n", "CONVERGED! delta= 0.077753; n= 0.030508; d_delta=9.74475e-07; d_n=9.15868e-07\n", "CONVERGED! delta= 0.073455; n= 0.030507; d_delta=8.60811e-07; d_n=9.62236e-07\n", "CONVERGED! delta= 0.068339; n= 0.030506; d_delta=4.81206e-07; d_n=9.50238e-07\n", "CONVERGED! delta= 0.062203; n= 0.030505; d_delta=2.90046e-07; d_n=9.58269e-07\n", "CONVERGED! delta= 0.054696; n= 0.030504; d_delta=9.79445e-07; d_n=6.09187e-07\n", "CONVERGED! delta= 0.045125; n= 0.030504; d_delta=9.86919e-07; d_n=2.58155e-07\n", "CONVERGED! delta= 0.031687; n= 0.030504; d_delta=9.94289e-07; d_n=1.28863e-07\n", "CONVERGED! delta= 0.001045; n= 0.030504; d_delta=9.99687e-07; d_n=3.50474e-09\n", "CONVERGED! delta= 0.000094; n= 0.030504; d_delta=9.99875e-07; d_n=3.9065e-10\n", "CONVERGED! delta= 0.000041; n= 0.030505; d_delta=8.33421e-07; d_n=9.61161e-07\n", "CONVERGED! delta= 0.000013; n= 0.030506; d_delta=3.71865e-07; d_n=9.94275e-07\n", "CONVERGED! delta= 0.000003; n= 0.030507; d_delta=1.02267e-07; d_n=9.81203e-07\n", "CONVERGED! delta= 0.000000; n= 0.030508; d_delta=1.80964e-08; d_n=9.70023e-07\n", "CONVERGED! delta= 0.000000; n= 0.030509; d_delta=1.29656e-09; d_n=9.60231e-07\n" ] } ], "source": [ "a_s=-1.0 # Scattering lenght\n", "N=1000 # number of atoms\n", "n=N/V\n", "Tv=np.linspace(0,0.15*eF(n)/kB,30) # temperatures\n", "delta=0.1\n", "mu=eF(n)\n", "\n", "kBT_per_eF=[]\n", "delta_per_eF=[]\n", "mu_per_eF=[]\n", "for T in Tv:\n", " # solve problem\n", " delta, mu, n, nk = solve_bcs(delta, mu, a_s, n, T, alpha=0.5, beta=0.5, epsd=1.0e-6, epsn=1.0e-6, maxiters=10000)\n", " # save data\n", " kBT_per_eF.append(kB*T/eF(n))\n", " delta_per_eF.append(delta/eF(n))\n", " mu_per_eF.append(mu/eF(n))" ] }, { "cell_type": "code", "execution_count": 9, "id": "4635496e", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot results \n", "\n", "# Expectation for Tc\n", "Tc=delta_per_eF[0]/1.76\n", "\n", "# delta vs temperature\n", "fig, ax = plt.subplots()\n", "ax.plot(kBT_per_eF, delta_per_eF, label=\"numerics\")\n", "plt.axvline(x=Tc, color=\"r\", linestyle=':')\n", "ax.set(xlabel=r'$k_BT/\\varepsilon_F$', ylabel=r'$\\Delta/\\varepsilon_F$')\n", "ax.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 10, "id": "fe662613", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Chemical potential vs temperature\n", "fig, ax = plt.subplots()\n", "ax.plot(kBT_per_eF, mu_per_eF, label=\"numerics\")\n", "plt.axvline(x=Tc, color=\"r\", linestyle=':')\n", "ax.set(xlabel=r'$k_BT/\\varepsilon_F$', ylabel=r'$\\mu/\\varepsilon_F$')\n", "ax.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "cc7545be", "metadata": {}, "source": [ "# Occupation probabilities" ] }, { "cell_type": "code", "execution_count": 11, "id": "80e0774c", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "CONVERGED! delta= 0.094110; n= 0.030519; d_delta=7.61682e-07; d_n=9.8579e-07\n", "CONVERGED! delta= 0.000007; n= 0.030518; d_delta=9.50305e-07; d_n=4.58599e-07\n" ] } ], "source": [ "a_s=-1.0 # Scattering lenght\n", "N=1000 # number of atoms\n", "n=N/V\n", "delta=0.1\n", "mu=eF(n)\n", "\n", "T=0.0 # temperature\n", "delta0, mu0, n0, nk0 = solve_bcs(delta, mu, a_s, n, T, alpha=0.5, beta=0.5, epsd=1.0e-6, epsn=1.0e-6, maxiters=10000)\n", "\n", "T=0.2*eF(n)/kB # temperature\n", "delta1, mu1, n1, nk1 = solve_bcs(delta, mu, a_s, n, T, alpha=0.5, beta=0.5, epsd=1.0e-6, epsn=1.0e-6, maxiters=10000)" ] }, { "cell_type": "code", "execution_count": 12, "id": "31a8a42a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot occupation probabilities\n", "fig, ax = plt.subplots()\n", "ax.plot(np.sqrt(k2v)/kF(n0), nk0, 'o', label=r'$k_B T/\\varepsilon_F=0.0$')\n", "ax.plot(np.sqrt(k2v)/kF(n1), nk1, 'o', label=r'$k_B T/\\varepsilon_F=0.2$')\n", "ax.set(xlabel=r'$k/k_F$', ylabel=r'$n(k)$')\n", "ax.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": 13, "id": "ab9017e0", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# plot occupation probabilities\n", "C=0.012\n", "nk_tail = C / k2v**2\n", "\n", "fig, ax = plt.subplots()\n", "ax.plot(np.sqrt(k2v)/kF(n0), nk0, 'o', label=r'numerics')\n", "ax.plot(np.sqrt(k2v)/kF(n0), nk_tail, label=r'$C/k^4$')\n", "ax.set(xlabel=r'$k/k_F$', ylabel=r'$n(k)$')\n", "ax.set_xlim([1.5,3.0])\n", "ax.set_ylim([1.0e-4,1.0e-2])\n", "plt.xscale(\"log\")\n", "plt.yscale(\"log\")\n", "ax.grid()\n", "plt.legend()\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "af04cc17", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3 (ipykernel)", "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": "3.10.11" } }, "nbformat": 4, "nbformat_minor": 5 }