guenp/aCMT

## aCMT
{
 "metadata": {
  "name": "",
  "signature": "sha256:81a558d85696d47c0f315555bae55044a150b661f4bf6f01cd04827d8abb9dc8"
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "heading",
     "level": 1,
     "metadata": {},
     "source": [
      "BCS theory and the Josephson effect"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{align}\n",
      "\\DeclareMathOperator{\\arcsinh}{arcsinh}\n",
      "\\newcommand{\\acreate}[1]{c_{#1\\uparrow}^{\\dagger}}\n",
      "\\newcommand{\\bcreate}[1]{c_{#1\\downarrow}^{\\dagger}}\n",
      "\\newcommand{\\ccreate}[1]{c_{#1\\uparrow\\downarrow}^{\\dagger}}\n",
      "\\newcommand{\\adestroy}[1]{c_{#1\\uparrow}}\n",
      "\\newcommand{\\bdestroy}[1]{c_{#1\\downarrow}}\n",
      "\\newcommand{\\cdestroy}[1]{c_{#1\\uparrow\\downarrow}}\n",
      "\\newcommand{\\ket}[1]{\\left|{#1}\\right\\rangle}\n",
      "\\newcommand{\\bra}[1]{\\left\\langle{#1}\\right|}\n",
      "\\end{align}"
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "Introduction"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In this notebook, I will derive the basics of BCS (Bardeen, Cooper and Schrieffer) theory using second quantization. This results in an equation for the temperature dependence of the superconducting gap. After this, I will go through a derivation of the DC and AC Josephson effect, using the wavefunction for the superconducting order parameter in two weak link-coupled superconducting systems."
     ]
    },
    {
     "cell_type": "heading",
     "level": 3,
     "metadata": {},
     "source": [
      "The basics of BCS"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Superconductivity arises when electrons are able to move through a material lattice with zero resistance. This is possible when electrons, instead of feeling a net repulsing force, they in fact attract each other, forming pairs. These Cooper pairs behave as bosons, hence being able to condense into the same, scatter-less state resulting in a macroscopic superconducting phase. The pairing occurs when under the right conditions, an electron moves through a lattice, and attracts a slight ripple of positively charged lattice atoms toward its path. Another electron moving in the opposite direction is attracted to that net positive charge. This scattering process can also be shown in a Feynman diagram."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image as IM\n",
      "i = IM(filename='pyfeyn.png', width=300)\n",
      "i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": 300
        }
       },
       "output_type": "pyout",
       "png": 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sol/z4WwySQFtouAgQIAAAQIECBAgQIAAAQIECBAgQIAAAQIECBAgUD6Beg9mE/m6CGeT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\nfGeBLJxwudSLvcC0vrJ8w2rzerN5wWNXDwRme9z6/TTGY+ZKyZI7pJ1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IIIAAAggggAAC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\njFOPHTtW1qxZY2wL+8p7770n7tSP2rbGjRuHvep5r5/Ob9erV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XD99dd7bspn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ltdQjYQI//fSTDB8+PD1Kdty4cVJcXByYQNOmTWXJkiVSpUqVwOrAhRFAAAEEEEAA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\nfwDooAPph+FK5gAAAABJRU5ErkJggg==\n",
       "prompt_number": 2,
       "text": [
        "<IPython.core.display.Image at 0x1058d1c10>"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Bardeen, Cooper and Schrieffer proposed a ground state ansatz in the grand canonical ensemble. Because electron pairs are boson-like particles, they are likely to all condense into the ground state. Their ansatz is a trial state with the pairs $(k \\uparrow, -k \\downarrow)$, described as a two-level system, being occupied with amplitude $v_{k}$ and unoccupied with amplitude $u_{k}$"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "\\ket\\psi_{BCS}=\\prod_{_{k}}(u_{k}+v_{k}\\ccreate{k})\\ket{0}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(1)</div>\n",
      "\n",
      "where $u_{k}$ and $v_{k}$ are real and can be found by requiring that $\\ket\\psi_{BCS}$ minimizes the energy. We require probabilities to add up to one such that $|u_{k}|^{2} + |v_{k}|^{2} = 1$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Setting up the Hamiltonian"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Consider a system of N pairs of fermions $\\alpha$ and $\\beta$, which in the case of BCS are spin up and down electrons. The free part of the Hamiltonian reads in second-quantization representation (in terms of creation operators $\\acreate{k}$ and $\\bcreate{k}$) as"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "H_{0} = \\sum\\limits_{k} \\epsilon_{k} (\\acreate{k} \\adestroy{k} + \\bcreate{k} \\bdestroy{k})\n",
      "\\end{equation}\n",
      "<div align=\"right\">(2)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $\\acreate{k} \\adestroy{k}$ ($\\bcreate{k} \\bdestroy{k}$) is a number operator which counts the number of spin up (down) particles with momentum $k$. $\\epsilon_{k}$ counts the kinetic energy for electrons with momentum $k$.\n",
      "\n",
      "The interaction part of the Hamiltonian includes an electron-electron attraction reduced to net zero-momentum pairing"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "V_{BCS} = -\\sum\\limits_{k',k} V_{k,k'} \\acreate{k} \\bcreate{-k} \\bdestroy{-k'} \\adestroy{k'}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(3)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "such that the pairing-hamiltonian $H_{BCS} = H_{0} + V_{BCS}$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This expression describes a second order scattering process in which two electrons with opposite spins and momenta $(k'\\uparrow,-k'\\downarrow)$ scatter into another pair with $(k\\uparrow, -k\\downarrow)$ with amplitude $-V_{k'k}$, which represents the strength of their interaction with lattice vibrations."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order for the lowest possible energy, the pairs must see an attractive potential - meaning, pairs from which the ground state is formed require zero momentum. This gives the creation operator of the time-reversed Cooper pair"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "\\ccreate{k} = \\acreate{k} \\bcreate{-k}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(4)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Writing the BCS hamiltonian in terms of the pair operators $\\cdestroy{k}$ and assuming V is k-independent gives"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "H_{BCS} = \\sum\\limits_{k\\sigma}\\epsilon n_{k \\sigma} - V\\sum\\limits_{k,k'}\\ccreate{k} \\cdestroy{k'}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(5)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $n_{k\\sigma}$ is the number operator for electrons with momentum $k$ and spin $\\sigma$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Minimization of the Hamiltonian mean-value $\\bra{\\psi_{BCS}} \\hat{H}_{BCS} \\ket{\\psi_{BCS}}$ in the grand canonical ensemble using the chemical potential $\\mu$ as Lagrange multiplier gives"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "\\hat{H}_{BCS} = H_{BCS} - \\mu \\hat{N} = \\hat{H}_{0} + V_{BCS}\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(6)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $\\hat{N}$ is the number operator $\\sum\\limits_{k} (\\acreate{k} \\adestroy{k} + \\bcreate{k} \\bdestroy{k})$ for both types of fermions."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can thus write equation (5) as"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "H^{'}_{BCS} = H_{BCS} - \\mu \\hat{N} = \\sum\\limits_{k\\sigma}\\xi_{k} n_{k \\sigma} - V \\sum\\limits_{k,k'}\\ccreate{k} \\cdestroy{k'}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(7)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $\\xi_{k} = \\frac{\\hbar^{2} k^{2}}{2m} - \\mu$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The second interaction term in equation (7), $\\ccreate{k}\\cdestroy{k'} = \\acreate{k} \\bcreate{-k} \\bdestroy{-k'} \\adestroy{k'}$ is not analytically solvable, but can be decoupled by mean field theory as follows"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "\\acreate{k} \\bcreate{-k} \\bdestroy{-k'} \\adestroy{k'}\n",
      "\\simeq\n",
      "\\langle \\acreate{k} \\bcreate{-k} \\rangle \\bdestroy{-k'} \\adestroy{k'}\n",
      "+\n",
      "\\acreate{k} \\bcreate{-k} \\langle \\bdestroy{-k'} \\adestroy{k'} \\rangle\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(8)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which gives the BCS mean-field Hamiltonian"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "H^{mf}_{BCS} = \\sum\\limits_{k\\sigma} \\xi_{k} c_{k \\sigma}^{\\dagger} c_{k \\sigma} - \\sum\\limits_{k}(\\Delta \\acreate{k} \\bcreate{-k} + \\Delta^{*} \\bdestroy{-k} \\adestroy{k})\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(9)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $\\Delta = V \\sum\\limits_{k} \\langle \\bdestroy{-k} \\adestroy{k} \\rangle$"
     ]
    },
    {
     "cell_type": "heading",
     "level": 6,
     "metadata": {},
     "source": [
      "Diagonalizing the Hamiltonian"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Hamiltonian can be written in matrix form\n",
      "\n",
      "\\begin{equation}\n",
      "H^{mf}_{BCS} = \\sum\\limits_{k} A_{k}^{\\dagger}\n",
      "\\begin{pmatrix}\n",
      "\\xi_{k} & -\\Delta \\\\\n",
      "-\\Delta^{*} & -\\xi_{-k}\n",
      "\\end{pmatrix}\n",
      "A_{k}\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(10)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where, by assuming that the crystal exhibits inversion symmetry $\\xi_{-k} = \\xi_{k}$. $A_{k}$ is the Nambu spinor\n",
      "\n",
      "\\begin{equation}\n",
      "A_{k}=\n",
      "\\begin{pmatrix}\n",
      "\\adestroy{k}\\\\\n",
      "\\bcreate{-k}\n",
      "\\end{pmatrix}\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(11)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The eigenvalues are $\\pm E_{k} = \\pm \\sqrt{\\xi_{k}^{2} + |\\Delta_{k}|^{2}}$. The Hamiltonian is diagonalized with a unitary transformation given by the Bogoliubov-Valatin transformation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "U =\n",
      "\\begin{pmatrix}\n",
      "u_{k} & v_{k} \\\\\n",
      "-v_{k}^{*} & u_{k}^{*}\n",
      "\\end{pmatrix}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(12)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where $|u_{k}|^{2} + |v_{k}|^2 = 1$ with $u_{k}v_{k} = \\frac{\\Delta}{2E_{k}}$ and"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "|u_{k}|^{2} = \\frac{1}{2}(1+\\frac{\\xi_{k}}{E_{k}}),\n",
      "\\end{equation}\n",
      "<div align=\"right\">(13)</div>\n",
      "\n",
      "\\begin{equation}\n",
      "|v_{k}|^{2} = \\frac{1}{2}(1-\\frac{\\xi_{k}}{E_{k}}).\n",
      "\\end{equation}\n",
      "<div align=\"right\">(14)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can now define the quasiparticle operators in the diagonal basis\n",
      "\\begin{equation}\n",
      "\\begin{pmatrix}\n",
      "\\gamma_{k \\uparrow} \\\\\n",
      "\\gamma_{-k \\downarrow}^{\\dagger}\n",
      "\\end{pmatrix}\n",
      "=\n",
      "U^{\\dagger}\n",
      "\\begin{pmatrix}\n",
      "\\adestroy{k} \\\\\n",
      "\\bcreate{-k}\n",
      "\\end{pmatrix}\n",
      "=\n",
      "\\begin{pmatrix}\n",
      "u_{k}^{*} & -v_{k} \\\\\n",
      "v_{k}^{*} & u_{k}\n",
      "\\end{pmatrix}\n",
      "\\begin{pmatrix}\n",
      "\\adestroy{k} \\\\\n",
      "\\bcreate{-k}\n",
      "\\end{pmatrix}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(15)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "as we now diagonalized the problem, the Hamiltonian will be\n",
      "\\begin{equation}\n",
      "H_{BCS} = \\sum\\limits_{k \\sigma} E_{k} \\gamma_{k \\sigma}^{\\dagger} \\gamma_{k \\sigma} + \\sum\\limits_{k} (\\xi_{k} - E_{k} + \\Delta \\langle \\acreate{k} \\bcreate{-k} \\rangle^{*})\n",
      "\\end{equation}\n",
      "<div align=\"right\">(16)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "or, since the second term is a constant\n",
      "\\begin{equation}\n",
      "H_{BCS} = E_{0} + \\sum\\limits_{k \\sigma} E_{k} \\gamma_{k \\sigma}^{\\dagger} \\gamma_{k \\sigma}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(17)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which is formally identical to the free part of the original Hamiltonian, except that now the number operator $n_{k \\sigma} = \\gamma_{k \\sigma}^{\\dagger} \\gamma_{k \\sigma}$ counts the number of free fermion excitations above the superconducting ground state with energy $E_{k} > 0$."
     ]
    },
    {
     "cell_type": "heading",
     "level": 5,
     "metadata": {},
     "source": [
      "Finding the gap equation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The Hamiltonian shows a minimum energy, or gap $\\Delta_{k}$ which also plays the role of the order parameter for the superconducting phase. We can now calculate the gap function"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "\\Delta = V\\sum\\limits_{k} \\langle \\adestroy{k} \\bdestroy{-k} \\rangle\\\\\n",
      "= V\\sum\\limits_{k} u_{k}v_{k} \\langle 1 - \\gamma^{\\dagger}_{k\\uparrow} \\gamma_{k\\uparrow} -\\gamma^{\\dagger}_{k\\downarrow}\\gamma_{k\\downarrow} \\rangle\\\\\n",
      "= V\\sum\\limits_{k} \\frac{\\Delta}{2E_{k}} (1-2f(E_{k}))\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(18)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "using the fact that $\\gamma^{\\dagger}$ and $\\gamma$ represent fermions and are therefore thermally distributed according to the Fermi distribution, such that $\\langle n_{k \\sigma} \\rangle = \\langle \\gamma^{\\dagger}_{k \\sigma} \\gamma_{k \\sigma} \\rangle = f(E_{k})$.\n",
      "By using the identity $1-2f(E_{k}) = tanh(\\frac{E_{k}}{2kT})$ we find the BCS gap equation"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "\\begin{equation}\n",
      "\\Delta = V\\sum\\limits_{k} \\frac{\\Delta}{2E_{k}} \\tanh(\\frac{E_{k}}{2kT})\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(19)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This equation can be solved numerically. The momentum sum can be changed to an integral in energy\n",
      "\\begin{equation}\n",
      "1 = VN(0)\\int^{\\omega_{D}}_{0} d\\xi \\frac{1}{E} \\tanh(\\frac{E}{2kT}),\n",
      "\\end{equation}\n",
      "with $E = \\sqrt{\\xi^{2} + |\\Delta|^{2}}$.\n",
      "<div align=\"right\">(20)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "at $T=T_{c}$, superconductivity is destroyed such that $\\Delta = 0$, meaning that $E \\rightarrow \\xi$ so that\n",
      "\n",
      "\\begin{equation}\n",
      "1 = VN(0)\\int^{\\omega_{D}}_{0} d\\xi \\frac{1}{\\xi} \\tanh(\\frac{\\xi}{2kT_{c}}),\n",
      "\\end{equation}\n",
      "<div align=\"right\">(21)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "and by approximation we find\n",
      "\\begin{equation}\n",
      "1 = VN(0) \\ln{\\frac{\\omega_{D}}{T_{c}}} \\rightarrow T_{c} \\simeq \\omega_{D} e^{-1/N_{0}V}.\n",
      "\\end{equation}\n",
      "<div align=\"right\">(22)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "For $T=0$ the gap equation reads\n",
      "\\begin{equation}\n",
      "VN(0)\\int^{\\omega_{D}}_{0} d\\xi \\frac{1}{E} = \\arcsinh{\\frac{\\omega_{D}}{\\Delta}} \\simeq \\ln{\\frac{2\\omega_{D}}{\\Delta}}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(23)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "such that\n",
      "\\begin{equation}\n",
      "\\Delta(0) = 2\\omega_{D}e^{-\\frac{1}{VN(0)}}\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(24)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "or\n",
      "\\begin{equation}\n",
      "\\frac{\\Delta(0)}{kT_{c}} = 1.76,\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(25)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which is the famous BCS ratio that holds for conventional s-wave superconductors."
     ]
    },
    {
     "cell_type": "heading",
     "level": 2,
     "metadata": {},
     "source": [
      "The Josephson effect"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Superconductivity is a macroscopic expression of a quantummechanically coherent phenomenon - meaning, we can define a macroscopic quantum wave function\n",
      "\n",
      "\\begin{equation}\n",
      "\\Psi(r,t) = \\Psi_{0}(r,t)e^{i\\phi(r,t)}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(26)</div>\n",
      "\n",
      "representing the superconducting order parameter, that describes the behavior of the entire ensemble of superconducting electrons in a superconductor. In the superconducting state, $\\Psi$ is nonzero, whilst above $T_{c}$ it vanishes. In a conventional s-wave superconductor, this order parameter is represented by the gap function."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "i = IM(filename='JJ.png', width=300)\n",
      "i"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {
        "png": {
         "width": 300
        }
       },
       "output_type": "pyout",
       "png": 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ZxZSQaARyB7X63Qd0dT5BX7cnZ+uac1iwOer/nBhglAjExnlh/fuj1MviCoWr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\n",
       "prompt_number": 3,
       "text": [
        "<IPython.core.display.Image at 0x104c65b50>"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "<b>Figure</b>: Schematic diagram of a Josephson junction, where the superconductors are connected with a bias voltage V. $\\Delta \\phi = \\phi_{L} - \\phi_{R}$ is the phase difference across the junction. [Source: ref 1]"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Using this macroscopic representation, consider two superconducting systems, couples by a think barrier of a metallic conductor, or a so-called weak link. The right side of the two systems evolves according to the Schr\u00f6dinger equation as\n",
      "\\begin{equation}\n",
      "i \\hbar \\frac{d\\Psi_{R}}{dt} = \\mu_{R} \\Psi_{R} + \\hbar \\chi \\Psi_{L}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(27)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "and likewise for the left side of the systems, where $\\mu_{L,R}$ is the chemical potential for the left (right) system.\n",
      "Entering equation (26) into (27) then gives\n",
      "\\begin{equation}\n",
      "i \\hbar \\frac{\\partial}{\\partial t} (\\Psi_{R,0}(r,t)e^{i\\phi_{R}(r,t)}) = \\mu_{R} \\Psi_{R,0}(r,t)e^{i\\phi_{R}(r,t)} + \\hbar \\chi \\Psi_{L,0}(r,t)e^{i\\phi_{L}(r,t)}\n",
      "\\end{equation}\n",
      "\\begin{equation}\n",
      "i \\frac{\\partial \\Psi_{R,0}(r,t)}{\\partial t} - \\Psi_{R,0}(r,t) \\frac{\\partial \\phi_{R} (r,t)}{\\partial t} = \\frac{\\mu_{R}}{\\hbar} \\Psi_{R,0}(r,t) + \\chi \\Psi_{L,0}(r,t)e^{i(\\phi_{L}(r,t)-\\phi_{R}(r,t))}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(28)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Taking the imaginary part on both sides\n",
      "\\begin{equation}\n",
      "\\frac{\\partial \\Psi_{R,0}(r,t)}{\\partial t} = - \\frac{\\partial \\Psi_{L,0}(r,t)}{\\partial t} = \\chi \\Psi_{L,0}(r,t) \\sin(\\Delta \\phi)\n",
      "\\end{equation}\n",
      "<div align=\"right\">(29)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "with $\\Delta \\phi = \\phi_{L}(r,t)-\\phi_{R}(r,t)$. Because the supercurrent density $J_{s} \\propto \\Psi$ ($= \\sqrt{n}=$ the Cooper pair density), we find\n",
      "\\begin{equation}\n",
      "J_{s} = J_{c} \\sin(\\Delta \\phi)\n",
      "\\end{equation}\n",
      "<div align=\"right\">(30)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "which is the Josephson current-phase relation. Consequently, combining the Schr\u00f6dinger equation for the right and left system and taking the real parts, we find\n",
      "\\begin{equation}\n",
      "\\frac{\\partial \\Delta \\phi_(r,t)}{\\partial t} = \\frac{\\Delta \\mu}{\\hbar}\n",
      "\\end{equation}\n",
      "<div align=\"right\">(31)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "where the bias $\\Delta \\mu = \\mu_{L} - \\mu_{R}$."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This result can also be obtained using the BCS ground state ansatz in equation (5).\n",
      "\n",
      "Consider two superconducting systems, where one is biased with a voltage V, which can be accounted for by a Gauge transformation $c_{k}^{\\dagger} \\rightarrow e^{i(e/\\hbar)\\int Vdt}c_{k}^{\\dagger}$ on each electron state.\n",
      "The superconducting state now changes as follows\n",
      "\n",
      "\\begin{equation}\n",
      "\\ket\\psi \\rightarrow \\prod_{_{k}}(u_{k}+v_{k} e^{i(e/\\hbar)\\int Vdt}\\acreate{k} e^{i(e/\\hbar)\\int Vdt} \\bcreate{-k})\\ket{0}\n",
      "=\n",
      "\\prod_{_{k}}(u_{k}+v_{k} e^{i(2e/\\hbar)\\int Vdt}\\acreate{k} \\bcreate{-k})\\ket{0}\n",
      "\\end{equation}\n",
      "\n",
      "<div align=\"right\">(32)</div>"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "This change can be written as\n",
      "\\begin{equation}\n",
      "\\frac{d\\phi}{dt} = \\frac{2eV}{\\hbar}.\n",
      "\\end{equation}\n",
      "<div align=\"right\">(33)</div>\n",
      "where the difference in chemical potential is proportional to the bias voltage, $\\Delta \\mu \\equiv 2eV$, which renders the phase evolution of the AC Josephson effect as found in equation (31)."
     ]
    },
    {
     "cell_type": "heading",
     "level": 4,
     "metadata": {},
     "source": [
      "References"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "[1] Superconducting Qubits and the Physics of Josephson Junctions, John M. Martinis and Kevin Osborne\n",
      "\n",
      "[2] The basics of BCS - and a bit more, Brian M\u00f8ller Andersen\n",
      "\n",
      "[3] BCS ansatz for superconductivity in the light of the Bogoliubov approach and the Richardson-Gaudin exact wave function, M. Combescot et al., Physica C 485, 47 (2013)"
     ]
    }
   ],
   "metadata": {}
  }
 ]
}