{ "cells": [ { "cell_type": "markdown", "id": "c21b2ffd", "metadata": {}, "source": [ "# Superconductivity with KWANT\n", "\n", "### © Jalil Varela-Manjarres, University of Delaware\n", "[PHYS824: Nanophysics & Nanotechnology](https://wiki.physics.udel.edu/phys824) " ] }, { "cell_type": "markdown", "id": "81d1450c", "metadata": {}, "source": [ "Some of the following examples were taken and adapted from https://tkwant.kwant-project.org/doc/dev/tutorial" ] }, { "cell_type": "markdown", "id": "6441636f", "metadata": {}, "source": [ "## What is covered in this notebook\n", " \n", "\n", " Physics background\n", "\n", " - Conductance of a NS-junction (Andreev reflection, superconducting gap)\n", "\n", "- 1D SNS-juntion with and without Barrier\n", "\n", "\n", "- 2D SAS-juntion with A being and altermagnetic d-metal (Pending)" ] }, { "cell_type": "code", "execution_count": 738, "id": "f5ffb676", "metadata": {}, "outputs": [], "source": [ "import kwant\n", "from matplotlib import pyplot\n", "import matplotlib.pyplot as plt\n", "import tinyarray\n", "import numpy as np\n", "tau_x = tinyarray.array([[0, 1], [1, 0]])\n", "tau_y = tinyarray.array([[0, -1j], [1j, 0]])\n", "tau_z = tinyarray.array([[1, 0], [0, -1]])" ] }, { "cell_type": "markdown", "id": "69bf9cc5", "metadata": {}, "source": [] }, { "cell_type": "markdown", "id": "223d1a42", "metadata": {}, "source": [ "The corresponding\n", "tight–binding Hamiltonian is\n", "\\begin{equation}\n", "\\hat H =\n", "\\sum_{i=-\\infty}^{+\\infty}\\sum_{\\sigma=\\uparrow,\\downarrow}\n", "\\left[\n", "e^{-i\\varphi_J(t)\\delta_{i,-1}}\n", "\\hat c_{i\\sigma}^\\dagger \\hat c_{i+1,\\sigma}\n", "+\n", "\\left(U\\delta_{i,0}-E_F\\right)\n", "\\hat c_{i\\sigma}^\\dagger \\hat c_{i\\sigma}\n", "\\right]\n", "+\n", "\\sum_{i=-\\infty}^{+\\infty}\n", "\\left[\n", "\\Delta (1-\\delta_{i,0})\\,\\hat c_{i\\uparrow}^\\dagger \\hat c_{i\\downarrow}^\\dagger\n", "+ \\text{h.c.}\n", "\\right].\n", "\\label{eq:H_SNS}\n", "\\end{equation}\n", "Here $\\hat c_{i,\\sigma}^\\dagger$ ($\\hat c_{i,\\sigma}$) creates (annihilates)\n", "a fermion with spin $\\sigma\\in\\{\\uparrow,\\downarrow\\}$ on site $i$.\n", "The time–dependent phase\n", "\\begin{equation}\n", "\\varphi_J(t) = \\frac{e}{\\hbar} \\int_0^t V_J(t')\\,\\mathrm{d}t'\n", "\\end{equation}\n", "is determined by the voltage drop $V_J(t)$ across the junction, which we\n", "assume to be located between the left superconducting lead and the central\n", "site. The parameter $\\Delta$ denotes the superconducting gap inside the\n", "leads, $U$ is a local barrier potential controlling the normal-state\n", "transmission probability $D$ of the junction, and $E_F$ is the Fermi\n", "energy. Within T-Kwant this Hamiltonian is treated almost as a standard\n", "normal-state tight-binding model; superconductivity simply doubles the\n", "local Hilbert space by introducing electron and hole degrees of freedom on\n", "each site.\n" ] }, { "cell_type": "markdown", "id": "b3af21f1", "metadata": {}, "source": [ "\n", "To make the notation more compact we introduce single-particle matrix\n", "elements\n", "\\begin{equation}\n", "h_{ij} = e^{-i\\varphi_J(t)\\delta_{i,-1}} \\delta_{i,j+1}\n", " + (U\\delta_{i,0}-E_F)\\delta_{ij},\n", "\\qquad\n", "\\Delta_{ij} = \\Delta (1-\\delta_{i,0}) \\delta_{ij}.\n", "\\label{eq:hij_Dij}\n", "\\end{equation}\n", "Strictly speaking, these expressions specify only the upper-triangular part\n", "of the Hamiltonian matrix; the lower-triangular part follows from Hermitian\n", "conjugation. With this definition the second-quantized Hamiltonian becomes\n", "\\begin{equation}\n", "\\hat H =\n", "\\sum_{i,j=-\\infty}^{+\\infty}\n", "\\left[\n", "h_{ij}\\bigl(\n", "\\hat c_{i\\uparrow}^\\dagger \\hat c_{j\\uparrow}\n", "+\n", "\\hat c_{i\\downarrow}^\\dagger \\hat c_{j\\downarrow}\n", "\\bigr)\n", "+\n", "\\Delta_{ij}\\hat c_{i\\uparrow}^\\dagger \\hat c_{j\\downarrow}^\\dagger\n", "+\n", "\\Delta_{ij}^\\ast \\hat c_{i\\downarrow}\\hat c_{j\\uparrow}\n", "\\right].\n", "\\label{eq:H_hDelta}\n", "\\end{equation}\n", "\n", "Using the fermionic anticommutation relations one can show that\n", "\\begin{equation}\n", "h_{ij}\\,\\hat c_i^\\dagger \\hat c_j\n", "= \\frac{1}{2}\n", "\\left(\n", "h_{ij}\\,\\hat c_i^\\dagger \\hat c_j\n", "- h_{ji}^\\ast\\,\\hat c_j \\hat c_i^\\dagger\n", "+ h_{ii}\\,\\delta_{ij}\n", "\\right),\n", "\\label{eq:fermion_identity}\n", "\\end{equation}\n", "which allows us to cast the Hamiltonian in Bogoliubov–de Gennes (BdG)\n", "matrix form,\n", "\\begin{equation}\n", "\\hat H =\n", "\\sum_{i,j=-\\infty}^{+\\infty}\n", "\\bigl(\\hat c_{i\\uparrow}^\\dagger,\\,\n", " \\hat c_{i\\downarrow}\\bigr)\n", "\\,H_{ij}\\,\n", "\\begin{pmatrix}\n", "\\hat c_{j\\uparrow}\\\\[2pt]\n", "\\hat c_{j\\downarrow}^\\dagger\n", "\\end{pmatrix},\n", "\\label{eq:H_BdG_matrix}\n", "\\end{equation}\n", "where $H_{ij}$ is the $2\\times2$ BdG Hamiltonian in Nambu (electron–hole)\n", "space." ] }, { "cell_type": "markdown", "id": "e735f26f", "metadata": {}, "source": [ "\n", "\n", "## Example 1:\"Superconductors\": orbitals, conservation laws and symmetries\n" ] }, { "cell_type": "markdown", "id": "77a45252", "metadata": {}, "source": [ "This example deals with superconductivity on the level of the Bogoliubov-de Gennes (BdG) equation. In this framework, the Hamiltonian is given as\n", "\n", " $$ H = \\begin{pmatrix}\n", " H_0 - \\mu & \\Delta \\\\\n", " \\Delta^\\dagger & \\mu - \\mathcal{T} H_0 \\mathcal{T}^{-1}\n", " \\end{pmatrix}$$\n", "\n", "where $H_0$ is the Hamiltonian of the system without\n", "superconductivity, $\\mu$ the chemical potential, $\\Delta$\n", "the superconducting order parameter, and $\\mathcal{T}$\n", "the time-reversal operator. The BdG Hamiltonian introduces\n", "electron and hole degrees of freedom (an artificial doubling -\n", "be aware of the fact that electron and hole excitations\n", "are related!), which we will need to include in our model with Kwant.\n", "\n", "For this we restrict ourselves to a simple spinless system without\n", "magnetic field, so that $\\Delta$ is just a number (which we\n", "choose real), and $\\mathcal{T}H_0\\mathcal{T}^{-1}=H_0^*=H_0.$\n", "Furthermore, note that the Hamiltonian has particle-hole symmetry\n", "$\\mathcal{P}$, i. e. $\\mathcal{P}H\\mathcal{P}^{-1}=-H.$\n", "\n" ] }, { "cell_type": "markdown", "id": "397a00e1", "metadata": {}, "source": [ "### N-S Junction " ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "4f51a523", "metadata": {}, "source": [ "Let us consider a system that consists of a normal lead on the left,\n", "a superconductor on the right, and a tunnel barrier in between:\n", "\n", "![image.png](attachment:image.png)\n", "\n", "\n", "Care must be taken when transport calculations are done with\n", "the BdG equation. Electrons and holes carry charge with\n", "opposite sign, such that it is necessary to separate the electron\n", "and hole degrees of freedom in the scattering matrix.\n", "In particular, the conductance of a N-S-junction is given as\n", "\n", "\n", " $$ G = \\frac{e^2}{h} (N - R_\\text{ee} + R_\\text{he})\\,,$$\n", "\n", "We implement the BdG Hamiltonian in Kwant using a 2x2 matrix structure\n", "for all Hamiltonian matrix elements.\n", "We start by declaring some parameters that will be used in the following code:\n" ] }, { "cell_type": "code", "execution_count": 739, "id": "9a31d977", "metadata": {}, "outputs": [], "source": [ "a = 1\n", "W, L = 10, 10\n", "barrier = 1.5\n", "barrierpos = (3, 4)\n", "mu = 0.4\n", "Delta = 0.1\n", "Deltapos = 4\n", "t = 1.0\n", "sep=4*t-mu" ] }, { "cell_type": "code", "execution_count": 740, "id": "3bce6cf7", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Start with an empty tight-binding system. On each site, there\n", "# are now electron and hole orbitals, so we must specify the\n", "# number of orbitals per site. The orbital structure is the same\n", "# as in the Hamiltonian.\n", "lat = kwant.lattice.square(norbs=2)\n", "syst = kwant.Builder()\n", "\n", "#### Define the scattering region. ####\n", "# The superconducting order parameter couples electron and hole orbitals\n", "# on each site, and hence enters as an onsite potential.\n", "# The pairing is only included beyond the point 'Deltapos' in the scattering region.\n", "syst[(lat(x, y) for x in range(Deltapos) for y in range(W))] = (4 * t - mu) * tau_z\n", "syst[(lat(x, y) for x in range(Deltapos, L) for y in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x\n", "\n", "# The tunnel barrier\n", "syst[(lat(x, y) for x in range(barrierpos[0], barrierpos[1])\n", " for y in range(W))] = (4 * t + barrier - mu) * tau_z\n", "\n", "# Hoppings\n", "syst[lat.neighbors()] = -t * tau_z\n", "\n", "kwant.plot(syst)\n", "plt.show()" ] }, { "cell_type": "code", "execution_count": null, "id": "6d678e96", "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "id": "0076a445", "metadata": {}, "source": [ "Note the argument ``norbs`` to `~kwant.lattice.square`. This is\n", "the number of orbitals per site in the discretized BdG Hamiltonian - of course,\n", "``norbs = 2``, since each site has one electron orbital and one hole orbital.\n", "It is necessary to specify ``norbs`` here, such that we may later separate the\n", "scattering matrix into electrons and holes. Aside from this, creating the system\n", "is syntactically equivalent to :ref:`spin example `.\n", "The only difference is that the Pauli matrices now act in electron-hole space.\n", "Note that the tunnel barrier is added by overwriting previously set\n", "on-site matrix elements.\n", "\n", "The superconducting order parameter is nonzero only in a part of the\n", "scattering region - the part to the right of the tunnel barrier. Thus,\n", "the scattering region is split into a superconducting part (the right\n", "side of it), and a normal part where the pairing is zero (the left side\n", "of it). The next step towards computing conductance is to attach leads.\n", "Let's attach two leads: a normal one to the left end, and a superconducting\n", "one to the right end. Starting with the left lead, we have:\n" ] }, { "cell_type": "code", "execution_count": 741, "id": "d8091778", "metadata": {}, "outputs": [ { "data": { "image/png": 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iwnXuS3AI2KABF+E4DjGmONQ1NYOz22AI0eP6tUp3pzUkklXJ/aGjUqmg6ulEr+XGnc/cWDdnJA5kj8mUYJIJwCQTgEkmAJNMACaZAEwyAZhkAjDJBGCSCcAkE4BJJgCTTAAmmQBMMgGYZAKwQQMDsPc6wI0KglpvANdjA+fj6+6URIFJBlB/qxPvF9bgYFEduMWvoe99qlyvHRvySpA+NwqJMcFuzVEIpCV3dNuReegSjpY1otcxxFA3bx8cLWvE0bJGmEK02LF8JkwhnjUuzRnIHpPbOnuwPLsQ/yxtGFrw97jSZMWy3edw4XqLDNmJC0nJ3XYH1uwvQtm3bbzaWW12rM4xo+LfVokykwaSkg+VfIvCKtd6pKXL7tJ7l92JIMlZWVlQqVTYuHGjSOnIw/7CGkHtCyr+g9qbHSJlIz0uSzabzcjOzsaMGTPEzEdySmpbcbnBIigGxwG554X9o8iJS2fXt2/fRlpaGvbs2YPXX39dUAKyF4aZsQQwzRcc59ilRvzmp1NEyEh6XJK8fv16LFq0CPPnzx9Rss1mg81m6/9ssQzuRXIXhgmeAowWIU6rCGWi5IK35H/84x8oKSmB2Wx2av2srCxs3bqVd2KS4eUtSpgeJy67PAVekuvq6vDSSy/h5MmT8PPzc6pNZmYmMjIy+j9bLBZERkb2f5a9MIyvOJJ1o9SixJEDXpKLi4tx48YNzJo1q39Zb28vCgoKsGvXLthsNnh7D96IGo0GGs3wlXLkLgxztKwBG/IuCo4zx6icyXC8JD/yyCO4dOnSoGXPPfccTCYTNm/efJdgT+SxaSEYr9XghtU28sr3QGjdETnhJVmr1SIuLm7QsoCAAAQHB9+13FNRe3theUIkdp5yfd7x5AmjMVdBDyxI3vFKT4rGeK1rxdZUKmDT/MkiZyQtgp9CffbZZyKkIS/jtBq8uzIBqdmFsNr4lWHc/LgJC6crp1AbQLQnA3eKth1cm4RQnXNXCd5eKry+NA5rPeQdFHwg/Tx5SmggTr38MI6U1iO3sGbI253BAb74eUIk0hINiBjj74YshcMKwwzgYm0rnlr1AlqsnXD02KD398bVzw7D18fzdnisMIyL3G8YA1XVWVi+u9U6zmj0SMF8Uf5fwBgRJpkATDIBmGQCMMkEYJIJwCQTgEkmAJNMACaZAEwyAZhkAjDJBGCSCcAkE4BJJgCTTAA2MuQ7Lje0IbewFo5HMhDKeYOzd8PR24Hjlxrx6NQJ8HHiLXCeCnnJJy434e+nr6Gk9tadBcFGDCzstO79EoQE+uEXiQasmRcDjY/nzxL5PqQlb88vx85PKkZcr8nShe355ThT0Yw9z86Gzl85k90AwsfkXacqnBI8kAvVLViVY0ZXT69EWUkDScnm6hb8+WS5S22La1rxpxNXRc5IWkhKfu+LakHtD5rr0NHNb3qNOyEn+YalCye/bhIUw2qz4/DFepEykh63n3jJXRiGMz0KbsaTguMcMNchLVEZc5TdLlnuwjBjf6SBVoQ4NRTqeCkVL7VzsxhHQknHZLf3ZNkLw2jE+ZMDRIojB27PVO7CMNkF1/DGsSuC4xj1ASJkIw/kdtdPx0fAV4T70KkJBhGykQdykoNHa7BweoigGLpRajw5M2zkFT0EcpIBYGVyNLxUrrdPnWOAn1o5DypISr7fMMbl4qfJE4Px8gJlVf8hKRkAVqfEIHOhCSoePTolVo/sZ2dDrbBny24/u3Yna+ZNxNSwQGQXVOFMZTOGq55i1AcgLdGAlcnRihw8QFoyAKTEjkNK7Dhcb25H3vka7PnwOGycF7geG/y4Luzbuh4psXqo+HR5D4NV//keMTEx/bdajUaj7NfxzsJnOypv38PgDZNMACaZAEwyAZhkAjDJBGCSCcAkE4BJJgCTTAAmmQBMMgGYZAIwyQRgkgnAJBOASSYA+eE/fXAch7PXboKb/GPowpPA9XSD81Oho9sOf19lbybyw3/aOnvwYVEd8s7Xoqq5/a7fazU+eCo+HOlJUZg0Xoz5kOLAZzuSllxadwurc8xovt094roqFbDlcRPWeMi7GtkYLycormlFanahU4IBgOOArONXsP2ksuqFAEQlN7V14fl9Reh0oYrPzlOVOKKgUhIAUck556rR0u5cDx6KnZ9UQOajnCB4Sc7KykJCQgK0Wi3Gjx+PpUuX4upVZe2+uu0OHDTXCYpR1dyOLypvipSR9PCSfPr0aaxfvx6FhYXIz8+H3W7HggUL0N5+91mpp3L8q0bcFNCL+9hfWC08GZngdQH4r3/9a9DnvXv3Yvz48SguLsZDDz3kUgJyV/9xxC8DJrmW60CKa24JT0YmBF3lt7W1AQDGjh077Do2mw02m63/s8Uy+G3jclf/0U9zQIxCEJauHhGiyIPLJ14cxyEjIwMPPvgg4uLihl0vKysLOp2u/ycyMtLVrxQFziFO1R61kFnsMuNyT96wYQPKyspw5syZe66XmZmJjIyM/s8Wi2WQaNmr/6jFOSsOHq0RJY4cuCT5hRdewMcff4yCggJERETcc12NRgONZvgNIveswa/q2/DEX+/9j+kMT8wIFSEbeeC1u+Y4Dhs2bMChQ4dw6tQp2XuhGMSF63BfZJCgGF4qIG2uMkouAjwlr1+/Hrm5ucjLy4NWq0VTUxOamprQ2dkpVX6SkC5Q0E9M4xEeNEqkbKSHl+Tdu3ejra0NDz/8MEJDQ/t/Dhw4IFV+krB0ZhjmTR7nUtvgAF+8smiqyBlJC69jspJu5d0LH28vvJUWj5V7L8Bc3ep0uzH+ary7MgHRCqrGBxC9dw3cqY2ZuzoRqXMMTlXou98QhI/WJQs+nrsD0s+T+2i+bcMB852BA/W3Bpxf2G14Zu4kpCdFIS5c574Eh4ANGnARjuMQY4pDXVMzOLsNhhA9rl+rdHdaQ8JnOyp78JLIqFQqqHo60Wu5ceczN/ztWiVB9phMCSaZAEwyAZhkAjDJBGCSCcAkE4BJJgCTTAAmmQBMMgGYZAIwyQRgkgnAJBOASSYAGzQwAHuvA9yoIKj1BnA9NnA+vu5OSRSYZAD1tzrxfmENDhbVgVv8Gvrep8r12rEhrwTpc6OQGBPs1hyFQFpyR7cdmYcu4WhZI3odQwx18/bB0bJGHC1rhClEix3LZ8IU4lnj0pyB7DG5rbMHy7ML8c/ShqEFf48rTVYs230OF663yJCduJCU3G13YM3+IpR928arndVmx+ocMyr+bZUoM2kgKflQybcorHKtR1q67Hj9f78ROSNpISl5f2GNoPYFFf9B7c0OkbKRHnKSS2pbcbnBMvKK94DjgNzzwv5R5MTtZ9eyF4aZsQQwzRcc59ilRvzmp1NEyEh63C5Z7sIwwVOA0SLEaRWhTJRckNtdw8tblDA9Tlx2eQpu78myF4bxFUeybpRalDhy4HbJcheGOVrWgA15FwXHmWNUzmQ4crvrx6aFYLxWeHkmoXVH5IScZLW3F5YnCCsYN3nCaMxV0AMLcpIBID0p2uXerFIBm+ZPFjkjaSEpeZxWg3dXJkCr4X9KsvlxExZOV06hNoCoZOBO0baDa5MQqvNzan1vLxVeXxqHtR7yDgo+uP3s2p1MCQ3EqZcfxpHSeuQW1gx5uzM4wBc/T4hEWqIBEWP83ZClcFhhmAFcrG3FU6teQIu1E44eG/T+3rj62WH4+njeDo8VhnGR+w1joKo6C8t3t1rHGY0eKZgvyv8LGCPCJBOASSYAk0wAJpkATDIBmGQCMMkEYJIJwCQTgEkmAJNMACaZAEwyAZhkAjDJBGCSCcBGhnzH5YY25BbWwvFIBkI5b3D2bjh6O3D8UiMenToBPk68Bc5TIS/5xOUm/P30NZTU3rqzINiIgYWd1r1fgpBAP/wi0YA182Kg8RFnLpWckJa8Pb8cOz+pGHG9JksXtueX40xFM/Y8Oxs6f+VMdgMIH5N3napwSvBALlS3YFWOGV09vRJlJQ0kJZurW/Dnk+UutS2uacWfTlwVOSNpcUnyW2+9BaPRCD8/P8yaNQuff/652HlJyntfVAtqf9Bch45uuzjJyABvyQcOHMDGjRvx29/+FhcvXkRKSgoWLlyI2tpaKfITnRuWLpz8uklQDKvNjsMX60XKSHp4z6BITExEfHw8du/e3b9sypQpWLp0KbKyskZs//2R/3IXhuFMj4Kb8aTgODMidPh4w4MiZOQaks2g6O7uRnFxMbZs2TJo+YIFC3D27Nkh29hsNthstkHJDUTuwjBjf6SBVoQ4NT/UOl7Nzc3o7e3FhAkTBi2fMGECmpqG3gVmZWVBp9P1/0RGCpsALhQvtXOzGEdCScdkl66TVSrVoM8cx921rI/MzExkZGT0f7ZYLINEy14YxoU5yUMRIFIcOeCVqV6vh7e391299saNG3f17j40Gg00muFn9ctdGCa74BreOHZFcByjPkCEbOSB1+7a19cXs2bNQn5+/qDl+fn5SE5OFjUxqXg6PgK+ItyHTk0wiJCNPPD+azMyMvDOO+/g3XffxTfffINNmzahtrYWa9eulSI/0QkercHC6SGCYuhGqfHkzLCRV/QQeB9YnnnmGdy8eROvvvoqGhsbERcXh2PHjiEqSjklj1YmR+P/fdkAV4vqpc4xwE+tnAcVZCsNvPN5lUt1q5MnBiNn1Ryo3fzokc92JHnvGgBWp8Qgc6EJw1wUDElKrB7Zz852u2C+KOc6QALWzJuIqWGByC6owpnKZgy3TzPqA5CWaMDK5GhFDh4gLRkAUmLHISV2HK43tyPvfA2+abTC0tUDP7U3wnR+eCo+Aimx+mHvAygB8pL7MOoD8NtFU92dhiQob9/D4A2TTAAmmQBMMgGYZALIfnbdd4Pt+4MHGPzo237O3LCUXbLVeuc9h+4ePPBDwWq1QqfT3XMd2e9dOxwONDQ0QKvVwmq1IjIyEnV1dR5VMbdvYIMn5fX9nDiOg9VqRVhYGLy87n3Ulb0ne3l5ISIiAsB/R5gEBgZ6zMYciCfmNTCnkXpwH+zEiwBMMgHcKlmj0eAPf/jDPceAuQNPzEtITrKfeDHkh+2uCcAkE4BJJgCTTACPkrxt2zYkJyfD398fQUFBbsnB0+ZeFxQUYPHixQgLC4NKpcKRI0d4x/Aoyd3d3Vi2bBnWrVvnlu/3xLnX7e3tuO+++7Br1y7Xg3AeyN69ezmdTif7986ZM4dbu3btoGUmk4nbsmWL7LkMBQDu8OHDvNt5VE92J31zrxcsWDBo+b3mXisFJvk7XJl7rRQkl/zHP/4RKpXqnj9FRUVSp+E0fOZeKwXJHzVu2LABy5cvv+c60dHRUqcxIq7MvVYKkkvW6/XQ6/VSf41gBs69/tnPfta/PD8/H0uWLHFjZsLxqBkUtbW1aGlpQW1tLXp7e1FaWgoAmDRpEkaPHi3592dkZCA9PR2zZ89GUlISsrOz3T73+vbt26isrOz/fP36dZSWlmLs2LEwGJycCC/6eb4AVqxYwQG46+fTTz+VLYe//e1vXFRUFOfr68vFx8dzp0+flu27h+LTTz8dcpusWLHC6RjsUSMB2CUUAZhkAjDJBGCSCcAkE4BJJgCTTAAmmQBMMgGYZAIwyQRgkgnwf7OF6zOSEv94AAAAAElFTkSuQmCC", "text/plain": [ "
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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#### Define the leads. ####\n", "# Left lead - normal, so the order parameter is zero.\n", "sym_left = kwant.TranslationalSymmetry((-a, 0))\n", "# Specify the conservation law used to treat electrons and holes separately.\n", "# We only do this in the left lead, where the pairing is zero.\n", "lead0 = kwant.Builder(sym_left, conservation_law=-tau_z)#, particle_hole=tau_y)\n", "lead0[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z\n", "lead0[lat.neighbors()] = -t * tau_z\n", "\n", "\n", "kwant.plot(lead0)\n", "plt.show()\n", "\n", "\n", "k = np.arange(-np.pi, np.pi, 0.01)\n", "fig = kwant.plotter.bands(lead0.finalized(), momenta=k, show=False);\n", "ax = fig.axes[0]\n", "ax.set_ylim(-2.0, 2.0);\n", "ax.axhline(0.4,ls=\"--\")" ] }, { "cell_type": "markdown", "id": "167a5556", "metadata": {}, "source": [ "Note the two new new arguments in `~kwant.builder.Builder`, ``conservation_law``\n", "and ``particle_hole``. For the purpose of computing conductance, ``conservation_law``\n", "is the essential one, as it allows us to separate the electron and hole degrees of\n", "freedom. Note that it is not necessary to specify ``particle_hole``\n", "in `~kwant.builder.Builder` to correctly compute the conductance in this example.\n", "We will discuss the argument ``particle_hole`` later on. First, let us\n", "discuss ``conservation_law`` in more detail.\n", "\n", "Observe that electrons and holes are uncoupled in the left (normal) lead, since\n", "the superconducting order parameter that couples them is zero.\n", "Consequently, we may view the electron and hole degrees of freedom as being\n", "conserved, and may therefore separate them in the Hamiltonian.\n", "\n", "In more technical terms, the conservation law implies that the Hamiltonian\n", "can be block diagonalized into uncoupled electron and hole blocks. Since\n", "the blocks are uncoupled, we can construct scattering states in each block\n", "independently. Of course, any scattering state from the electron (hole) block\n", "is entirely electron (hole) like. As a result, the scattering matrix separates\n", "into blocks that describe the scattering between different types of carriers,\n", "such as electron to electron, hole to electron, et cetera.\n", "\n", "As we saw above, conservation laws in Kwant are specified with the\n", "``conservation_law`` argument in `~kwant.builder.Builder`.\n", "Specifically, ``conservation_law`` is a matrix that acts on a single *site*\n", "and it must in addition have integer eigenvalues.\n", "Of course, it must also commute with the onsite Hamiltonian and hoppings\n", "to adjacent sites. Internally, Kwant then uses the eigenvectors of the\n", "conservation law to block diagonalize the Hamiltonian. Here, we've specified\n", "the conservation law $-\\sigma_z$, such that the eigenvectors with\n", "eigenvalues $-1$ and $1$ pick out the electron and hole\n", "blocks, respectively. Internally in Kwant, the blocks are stored in the order\n", "of ascending eigenvalues of the conservation law.\n", "\n", "In order to move on with the conductance calculation, let's attach the second\n", "lead to the right side of the scattering region:" ] }, { "cell_type": "code", "execution_count": 742, "id": "c6160c79", "metadata": {}, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 742, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Right lead - superconducting, so the order parameter is included.\n", "sym_right = kwant.TranslationalSymmetry((a, 0))\n", "lead1 = kwant.Builder(sym_right)\n", "lead1[(lat(0, j) for j in range(W))] = (4 * t - mu) * tau_z + Delta * tau_x\n", "lead1[lat.neighbors()] = -t * tau_z\n", "\n", "\n", "k = np.arange(-np.pi, np.pi, 0.01)\n", "fig = kwant.plotter.bands(lead1.finalized(), momenta=k, show=False);\n", "ax = fig.axes[0]\n", "ax.set_ylim(-1.0, 1.0);\n", "\n", "#ax.axhline(0.0,ls=\"--\")\n", "ax.axhline(0.1,ls=\"--\")\n", "ax.axhline(-0.1,ls=\"--\")\n", "\n" ] }, { "cell_type": "code", "execution_count": 213, "id": "40e8a148", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#### Attach the leads and finalize the system. ####\n", "syst.attach_lead(lead0)\n", "syst.attach_lead(lead1)\n", "\n", "syst = syst.finalized()\n", "\n", "#plt.figure()\n", "kwant.plot(syst)\n", "plt.show()" ] }, { "cell_type": "markdown", "id": "4117c26b", "metadata": {}, "source": [ "The second (right) lead is superconducting, such that the electron and hole\n", "blocks are coupled. Of course, this means that we can not separate them into\n", "uncoupled blocks as we did before, and therefore no conservation law is specified.\n", "\n", "Kwant is now aware of the block structure of the Hamiltonian in the left lead.\n", "This means that we can extract transmission and reflection amplitudes not only\n", "into the left lead, but also between different conservation law blocks in\n", "the left lead. Generally if leads :math:`i` and :math:`j` both have a conservation\n", "law specified, ``smatrix.transmission((i, a), (j, b))`` gives us\n", "the scattering probability of carriers from block :math:`b` of lead :math:`j`, to\n", "block :math:`a` of lead :math:`i`. In our example, reflection from electrons to\n", "electrons in the left lead is thus ``smatrix.transmission((0, 0), (0, 0))`` (Don't get\n", "confused by the fact that it says ``transmission`` -- transmission\n", "into the same lead is reflection), and reflection from electrons to holes\n", "is ``smatrix.transmission((0, 1), (0, 0))``:" ] }, { "cell_type": "code", "execution_count": 214, "id": "0ba4f19d", "metadata": {}, "outputs": [], "source": [ "def plot_conductance(syst, energies):\n", " # Compute conductance\n", " data = []\n", " for energy in energies:\n", " smatrix = kwant.smatrix(syst, energy)\n", " # Conductance is N - R_ee + R_he\n", " data.append(smatrix.submatrix((0, 0), (0, 0)).shape[0] -\n", " smatrix.transmission((0, 0), (0, 0)) +\n", " smatrix.transmission((0, 1), (0, 0)))\n", " pyplot.figure()\n", " pyplot.plot(energies, data)\n", " pyplot.xlabel(\"energy [t]\")\n", " pyplot.ylabel(\"conductance [e^2/h]\")\n", " plt.axvline(0.1,ls=\"--\")\n", " \n", " pyplot.show()\n", " " ] }, { "cell_type": "code", "execution_count": 215, "id": "00bfb93a", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_conductance(syst, energies=[0.002 * i for i in range(-10, 100)])" ] }, { "cell_type": "code", "execution_count": 216, "id": "b6a6d3f5", "metadata": {}, "outputs": [], "source": [ "def plot_reflection(syst, energies):\n", " # Compute conductance\n", " data_refle_ee = []\n", " data_refle_hh = []\n", " data_refle_eh = []\n", "\n", " \n", " for energy in energies:\n", " smatrix = kwant.smatrix(syst, energy)\n", " # Conductance is N - R_ee + R_he\n", " data_refle_ee.append(smatrix.transmission((0, 0), (0, 0)) )\n", " data_refle_hh.append(smatrix.transmission((0, 1), (0, 1)) )\n", " data_refle_eh.append(smatrix.transmission((0, 0), (0, 1)) )\n", " \n", "# data_trans_ee.append(smatrix.transmission((0, 0), (1, 0)) )\n", "# data_trans_hh.append(smatrix.transmission((0, 1), (1, 1)) )\n", "# data_trans_eh.append(smatrix.transmission((0, 0), (1, 1)) )\n", " \n", " pyplot.figure()\n", " pyplot.plot(energies, data_refle_ee,label=r\"R_ee\")\n", " #pyplot.plot(energies, data_refle_hh,label=r\"R_hh\")\n", " pyplot.plot(energies, data_refle_eh,label=r\"R_eh\")\n", " pyplot.xlabel(\"energy [t]\")\n", " pyplot.ylabel(\"Reflection\")\n", " pyplot.legend()\n", " pyplot.show()\n", " \n", " \n", "def plot_transmission(syst, energies):\n", " # Compute conductance\n", " data_trans_ee = []\n", " data_trans_hh = []\n", " data_trans_eh = []\n", "\n", " \n", " for energy in energies:\n", " smatrix = kwant.smatrix(syst, energy)\n", " # Conductance is N - R_ee + R_he\n", "# data_refle_ee.append(smatrix.transmission((0, 0), (0, 0)) )\n", "# data_refle_hh.append(smatrix.transmission((0, 1), (0, 1)) )\n", "# data_refle_eh.append(smatrix.transmission((0, 0), (0, 1)) )\n", " \n", " data_trans_ee.append(smatrix.transmission((1, 0), (0, 0)) )\n", " #data_trans_hh.append(smatrix.transmission((1, 1), (0, 1)) )\n", " data_trans_eh.append(smatrix.transmission((1, 0), (0, 1)) )\n", " \n", " pyplot.figure()\n", " pyplot.plot(energies, data_trans_ee,label=r\"T_ee\")\n", " #pyplot.plot(energies, data_refle_hh,label=r\"R_hh\")\n", " pyplot.plot(energies, data_trans_eh,label=r\"T_eh\")\n", " pyplot.xlabel(\"energy [t]\")\n", " pyplot.ylabel(\"Trasmission\")\n", " pyplot.legend()\n", " pyplot.show()\n", " \n" ] }, { "cell_type": "code", "execution_count": 217, "id": "9e1578de", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_reflection(syst, energies=[0.002 * i for i in range(-10, 100)])" ] }, { "cell_type": "code", "execution_count": 218, "id": "a5dc6e9b", "metadata": { "scrolled": true }, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot_transmission(syst, energies=[0.002 * i for i in range(-10, 100)])" ] }, { "cell_type": "markdown", "id": "8a054ea9", "metadata": {}, "source": [ "## S-N-S Junction in 1D system " ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "1e8cd719", "metadata": {}, "source": [ "![image.png](attachment:image.png)\n", "\n", "\n", "We consider a short, ballistic S--N--S junction with a single perfectly\n", "transmitting channel ($T = 1$). The left and right superconducting\n", "electrodes have the same gap $\\Delta$ but different phases, $-\\phi/2$\n", "and $+\\phi/2$, respectively. We focus on subgap energies $|E| < \\Delta$.\n", "\n", "For energies inside the gap, quasiparticles cannot propagate in the bulk\n", "of the superconductors and are instead Andreev reflected at the\n", "interfaces. An incident electron from the normal region is retroreflected\n", "as a hole with the Andreev reflection amplitude\n", "$\n", "r_A(E) = e^{-i \\arccos(E/\\Delta)}.\n", "$\n", "At the opposite interface, the hole is converted back into an electron\n", "with the same magnitude of phase shift.\n", "\n", " We neglect \n", "(i) normal reflection at the interfaces and \n", "(ii) the dynamical phase accumulated in the normal region (its length is\n", "much shorter than the superconducting coherence length). A closed\n", "electron--hole orbit inside the junction then consists of:\n", "\n", "\n", "- two Andreev reflections, one at each S/N interface, giving a total\n", " Andreev phase $2 \\arccos(E/\\Delta)$;\n", "- the superconducting phase difference $\\phi$ picked up between the\n", " two electrodes.\n", "\n", "\n", "The quantization condition for an Andreev bound state is that the total\n", "phase acquired by an electron--hole loop is an integer multiple of $2\\pi$:\n", "$\n", "2 \\arccos(E/\\Delta) + \\phi = 2\\pi n, \\qquad n \\in \\mathbb{Z}.\n", "$\n", "Solving for $E$,\n", "\n", "$$\n", "\\arccos(E/\\Delta) = \\pi n - \\frac{\\phi}{2}\n", "\\;\\Rightarrow\\;\n", "\\frac{E}{\\Delta} = \\cos\\!\\Bigl(\\pi n - \\frac{\\phi}{2}\\Bigr)\n", " = (-1)^n \\cos\\!\\frac{\\phi}{2}.\n", "$$\n", "\n", "Even and odd $n$ simply correspond to the two branches of the spectrum,\n", "so we can write the Andreev bound state energies as\n", "$$\n", "E_\\pm(\\phi) = \\pm \\Delta \\cos\\frac{\\phi}{2}.\n", "$$\n", "\n", "This is the dispersion of Andreev bound states in a short,\n", "perfectly transmitting Josephson junction\n" ] }, { "cell_type": "code", "execution_count": 745, "id": "b5531e4d", "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "text/plain": [ "" ] }, "execution_count": 745, "metadata": {}, "output_type": "execute_result" } ], "source": [ "lat1d = kwant.lattice.chain(norbs=2)\n", "\n", "def make_sns_1d(phi,\n", " LS=4, # SC Left\n", " LW=1, # Central region\n", " RS=4, # SC Right\n", " mu=0.0, Delta=0.1, t=1.0):\n", " \"\"\"\n", " SNS 1D finito (sin leads):\n", " - onsite normal: -mu * tau_z\n", " - hopping: -t * tau_z\n", " - SC izquierda: Delta * e^{-i phi/2}\n", " - SC derecha: Delta * e^{+i phi/2}\n", " \"\"\"\n", " syst = kwant.Builder()\n", "\n", " Ltot = LS + LW + RS\n", "\n", " for x in range(Ltot):\n", " # S1: x < LS\n", " if x < LS:\n", " Δ = Delta * np.exp(-0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", " # N: LS <= x < LS+LW\n", " elif LS <= x < LS + LW:\n", " onsite = -mu * tau_z\n", " # S2: x >= LS+LW\n", " else:\n", " Δ = Delta * np.exp(+0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", "\n", " syst[lat1d(x)] = onsite\n", "\n", " # Hoppings 1D (vecinos a distancia 1)\n", " syst[lat1d.neighbors()] = -t * tau_z\n", "\n", " return syst.finalized()\n", "\n", "syst_test = make_sns_1d(0.0)\n", "kwant.plot(syst_test)\n", "plt.show()\n", "\n", "make_sns_1d(0.0)" ] }, { "cell_type": "code", "execution_count": 751, "id": "946784b7", "metadata": {}, "outputs": [ { "data": { "image/png": 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"text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "Delta = 0.1\n", "t = 1.0\n", "mu = 0.0\n", "LS, LW, RS = 40, 1, 40\n", "\n", "phi_list = np.linspace(-2*np.pi, 2*np.pi, 101)\n", "E_num = np.full_like(phi_list, np.nan, dtype=float)\n", "\n", "k_eigs = 12 # nº de autovalores alrededor de 0\n", "\n", "for i, phi in enumerate(phi_list):\n", " syst_f = make_sns_1d(phi, LS=LS, LW=LW, RS=RS,\n", " mu=mu, Delta=Delta, t=t)\n", "\n", " H = syst_f.hamiltonian_submatrix(sparse=True)\n", " evals, evecs = sla.eigsh(H, k=k_eigs, sigma=0.0)\n", " evals = np.real(evals)\n", "\n", " # ordenamos por |E| y tomamos el más cercano a 0\n", " evals_sorted = sorted(evals, key=lambda E: abs(E))\n", " E_closest = evals_sorted[0]\n", "\n", " E_num[i] = abs(E_closest)\n", "\n", "E_analytic_abs = np.abs(Delta * np.cos(phi_list / 2.0))\n", "\n", "plt.figure(figsize=(5,4))\n", "plt.plot(phi_list, E_num, 'o', label='|E_num(φ)|')\n", "plt.plot(phi_list, E_analytic_abs, '-', label=r'$|\\Delta \\cos(\\phi/2)|$')\n", "plt.xlabel(r'$\\phi$')\n", "plt.ylabel(r'$|E(\\phi)|$')\n", "##plt.title('SNS 1D corto: ABS numérico vs analítico')\n", "plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "d511053d", "metadata": {}, "source": [ "### Phase dependent current thorugh adiabatic variations \n" ] }, { "cell_type": "markdown", "id": "5d8839dc", "metadata": {}, "source": [ "In a Josephson junction the current is the rate of change of the number\n", "of Cooper pairs, $I = 2e\\, d\\langle N\\rangle/dt$, while the phase\n", "difference $\\phi$ is the variable conjugate to $N$. In a Josephson system, the phase $\\phi$ is\n", "canonically conjugate to the number of transferred pairs, which is\n", "encoded in the commutation relation\n", "$$\n", "[\\hat \\phi, \\hat N_R] = 2i,\n", "$$\n", "(up to conventions for factors of 2). This implies that the dependence\n", "of the Hamiltonian on $\\phi$ is equivalent to coupling to the number\n", "operator. One can then rewrite the commutator as a derivative with\n", "respect to $\\phi$:\n", "$$\n", "[\\hat H(\\phi), \\hat N_R]\n", "= -\\,2i\\,\\frac{\\partial \\hat H(\\phi)}{\\partial \\phi}.\n", "$$\n", "Combining this with the Heisenberg equation gives\n", "$$\n", "\\hat I = 2e\\,\\frac{d\\hat N}{dt}\n", " = -\\frac{2e}{\\hbar}\\frac{\\partial \\hat H}{\\partial \\phi},\n", "$$\n", "so that for an eigenstate with energy $E(\\phi)$ one obtains\n", "$$\n", "I(\\phi) = -\\frac{2e}{\\hbar}\\frac{\\partial E(\\phi)}{\\partial \\phi}.\n", "$$\n", "Experimentally, the AC Josephson relation $d\\phi/dt = 2eV/\\hbar$\n", "confirms this conjugate nature of phase and particle number:\n", "a DC voltage $V$ makes the phase wind linearly in time, and the\n", "resulting time-dependent current $I(\\phi(t))$ is the measurable\n", "signature of the transfer of Cooper pairs." ] }, { "cell_type": "markdown", "id": "bfb7a26c", "metadata": {}, "source": [ "In thermal equilibrium, the supercurrent in a short Josephson junction\n", "can be expressed in terms of the phase-dependent Andreev bound state (ABS)\n", "energies $E_n(\\phi)$ as\n", "$$\n", "I(\\phi) = -\\frac{2e}{\\hbar}\\sum_n\n", "\\frac{\\partial E_n(\\phi)}{\\partial \\phi}\\, f\\!\\bigl(E_n(\\phi)\\bigr),\n", "$$\n", "where $f(E)$ is the Fermi-Dirac distribution and the factor $2e$ reflects\n", "the charge of a Cooper pair.\n", "\n", "For a single perfectly transparent channel ($T=1$) in a short junction,\n", "the ABS spectrum is\n", "$$\n", "E_\\pm(\\phi) = \\pm \\Delta \\cos\\frac{\\phi}{2}.\n", "$$\n", "At zero temperature, only the lower branch $E_-(\\phi)$ is occupied\n", "($f(E_-) = 1$, $f(E_+) = 0$). The current is then entirely carried by this\n", "state:\n", "$$\n", "I(\\phi) = -\\frac{2e}{\\hbar}\\,\\frac{\\partial E_-(\\phi)}{\\partial \\phi}\n", " = -\\frac{2e}{\\hbar}\\,\\frac{\\partial}{\\partial \\phi}\n", " \\bigl[-\\Delta \\cos(\\phi/2)\\bigr].\n", "$$\n", "Taking the derivative, we obtain\n", "$$\n", "I(\\phi) = \\frac{e\\Delta}{\\hbar}\\,\\sin\\frac{\\phi}{2}.\n", "$$\n", "\n", "This expression is valid for the short-junction limit\n", "and for the phase interval where the branch $E_-(\\phi)$ is the\n", "ground state (typically $0 < \\phi < \\pi$). More generally, one\n", "must account for the $2\\pi$-periodicity and the possibility of\n", "level crossings, which leads to a current-phase relation with\n", "a cusp at $\\phi = \\pi$." ] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "id": "bcbc55a7", "metadata": {}, "source": [ "![image.png](attachment:image.png)" ] }, { "cell_type": "code", "execution_count": 758, "id": "158402a4", "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "#phi_list = np.linspace(, 2*np.pi, 101)\n", "\n", "I_num = np.full_like(phi_list, np.nan, dtype=float)\n", "dphi = phi_list[1] - phi_list[0]\n", "\n", "for i in range(1, len(phi_list)-1):\n", " if np.isfinite(E_num[i-1]) and np.isfinite(E_num[i+1]):\n", " I_num[i] = (E_num[i+1] - E_num[i-1]) / (2*dphi)\n", "\n", "\n", "phi_list_n = np.linspace(-np.pi, np.pi, 101)\n", "I_analytic = -(Delta / 2.0) * np.sin(phi_list_n / 2.0)\n", "\n", "mask = np.isfinite(I_num)\n", "phi_mask = phi_list[mask]\n", "phin_mask = phi_list_n[mask]\n", "I_num_norm = I_num[mask] / np.nanmax(np.abs(I_num[mask]))\n", "I_an_norm = I_analytic[mask] / np.max(np.abs(I_analytic[mask]))\n", "\n", "plt.figure(figsize=(5,4))\n", "plt.plot(phi_mask, -I_num_norm, 'o-', label='I_num')\n", "plt.plot(phin_mask, -I_an_norm, '-', label='I_analytic')\n", "plt.xlabel(r'$\\phi$')\n", "plt.ylabel('I')\n", "##plt.title('Forma de I(φ) ~ dE/dφ: numérico vs analítico')\n", "##plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "code", "execution_count": 729, "id": "5f9050a7", "metadata": {}, "outputs": [], "source": [ "# ---------- Normal chain (spinless) para T ----------\n", "lat_n = kwant.lattice.chain(norbs=2)\n", "def make_normal_barrier_1d(Vb, L=1, mu=0.0, t=1.0):\n", " \"\"\"\n", " Inifite Chain with a barrier Vb of one site in the central region\n", " \"\"\"\n", " syst = kwant.Builder()\n", " # Región de scattering: L sitios, barrera en el centro\n", " for x in range(L):\n", " onsite = -mu\n", " if x == L // 2:\n", " onsite += Vb\n", " syst[lat_n(x)] = onsite\n", "\n", " syst[lat_n.neighbors()] = -t\n", "\n", " # Lead izquierdo\n", " sym_left = kwant.TranslationalSymmetry([-1])\n", " leadL = kwant.Builder(sym_left)\n", " leadL[lat_n(0)] = -mu\n", " leadL[lat_n.neighbors()] = -t\n", "\n", " # Lead derecho\n", " sym_right = kwant.TranslationalSymmetry([+1])\n", " leadR = kwant.Builder(sym_right)\n", " leadR[lat_n(0)] = -mu\n", " leadR[lat_n.neighbors()] = -t\n", "\n", " syst.attach_lead(leadL)\n", " syst.attach_lead(leadR)\n", "\n", " return syst.finalized()\n", "\n", "\n", "def transm(Vb, mu=0.0, t=1.0, L=1, E=0.0):\n", " \"\"\"\n", " Transmission with a barrier Vb.\n", " \"\"\"\n", " systN = make_normal_barrier_1d(Vb, L=L, mu=mu, t=t)\n", " sm = kwant.smatrix(systN, energy=E)\n", " T = sm.transmission(1, 0) # lead 0 -> lead 1\n", " return T\n" ] }, { "cell_type": "code", "execution_count": 730, "id": "d9c3a098", "metadata": {}, "outputs": [], "source": [ "# ---------- BdG: SNS 1D corta con barrera Vb en la parte N ----------\n", "\n", "\n", "lat1d = kwant.lattice.chain(norbs=2)\n", "\n", "def make_sns_1d(phi,\n", " LS=4, # longitud SC izquierda\n", " LW=1, # longitud N (1 sitio)\n", " RS=4, # longitud SC derecha\n", " mu=0.0, Delta=0.1, t=1.0,\n", " Vb=0.0):\n", " \"\"\"\n", " SNS 1D finita (sin leads):\n", " - SC izquierda: Δ e^{-i φ/2}\n", " - N central: -mu τ_z + Vb τ_z\n", " - SC derecha: Δ e^{+i φ/2}\n", " \"\"\"\n", " syst = kwant.Builder()\n", " Ltot = LS + LW + RS\n", " for x in range(Ltot):\n", " # S1: x < LS\n", " if x < LS:\n", " Δ = Delta * np.exp(-0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", " # N (weak link, 1D, con barrera Vb)\n", " elif LS <= x < LS + LW:\n", " onsite = -mu * tau_z + Vb * tau_z\n", " # S2: x >= LS+LW\n", " else:\n", " Δ = Delta * np.exp(+0.5j * phi)\n", " onsite = -mu * tau_z + (Δ.real * tau_x - Δ.imag * tau_y)\n", " syst[lat1d(x)] = onsite\n", " # hoppings 1D\n", " syst[lat1d.neighbors()] = -t * tau_z\n", "\n", " return syst.finalized()\n" ] }, { "cell_type": "markdown", "id": "f7c3f6f4", "metadata": {}, "source": [ "### Generalization when a weak barrier is included" ] }, { "cell_type": "markdown", "id": "0f7bb8c6", "metadata": {}, "source": [ "Consider a short, single-channel S–N–S junction with normal-state\n", "transmission probability $T$ (and reflection $R = 1 - T$). In the\n", "superconducting leads we assume a real, energy-independent gap $\\Delta$ and\n", "phases $\\pm \\phi/2$ on the left and right superconductors.\n", "\n", "\n", "For subgap energies $|E| < \\Delta$, quasiparticles cannot propagate in the\n", "bulk of the superconductors and are instead Andreev reflected at each\n", "S/N interface. The Andreev reflection amplitude can be written as\n", "$\n", "r_A(E) = e^{-i\\arccos(E/\\Delta)}\\,,\n", "$\n", "so that an electron converts into a hole (and vice versa) with a phase shift\n", "$-\\arccos(E/\\Delta)$.\n", "\n", "\n", "\n", "A bound state corresponds to a closed electron–hole orbit which picks up a\n", "total phase that is an integer multiple of $2\\pi$. For a short junction\n", "(the normal region length $L$ much smaller than the coherence length),\n", "we can neglect the energy dependence of the normal-region scattering\n", "matrix and characterize it by a single transmission $T$. The closed\n", "electron–hole loop acquires:\n", "\n", "\n", "\n", "1. Two Andreev reflection phases, one at each interface:\n", " \\[\n", " 2 \\arccos(E/\\Delta),\n", " \\]\n", "2. The superconducting phase difference $\\phi$ between the two leads,\n", "3. A normal-scattering phase that depends on $T$." ] }, { "cell_type": "code", "execution_count": 743, "id": "e33bc024", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "T = 0.39024390243902457\n" ] }, { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Parámetros físicos\n", "Delta = 0.1\n", "t = 1.0\n", "mu = 0.0\n", "LS, LW, RS = 100, 1, 100 # junta corta\n", "Vb = 2.5 # fuerza de la barrera (ajusta a gusto)\n", "E_F = 0.0 # Fermi ~ 0 en este modelo (mu=0)\n", "\n", "# 1) Transparencia normal T para este Vb\n", "T_normal = transm(Vb, mu=mu, t=t, L=1, E=E_F)\n", "print(\"T =\", T_normal)\n", "\n", "# 2) ABS numérico vs φ en el estado superconducting\n", "phi_list = np.linspace(0, 2*np.pi, 101)\n", "E_num = np.full_like(phi_list, np.nan, dtype=float)\n", "\n", "#k_eigs = 12 # nº de autovalores alrededor de 0\n", "\n", "for i, phi in enumerate(phi_list):\n", " syst_f = make_sns_1d(phi, LS=LS, LW=LW, RS=RS,\n", " mu=mu, Delta=Delta, t=t,\n", " Vb=Vb)\n", "\n", " H = syst_f.hamiltonian_submatrix(sparse=True)\n", " evals, evecs = sla.eigsh(H, k=k_eigs, sigma=0.0)\n", " evals = np.real(evals)\n", "\n", " # nivel más cercano a 0 en |E|\n", " evals_sorted = sorted(evals, key=lambda E: abs(E))\n", " E_closest = evals_sorted[0]\n", " E_num[i] = abs(E_closest)\n", "\n", "# 3) Analytical expression\n", "E_analytic_abs = Delta * np.sqrt(1.0 - T_normal * np.sin(phi_list / 2.0)**2)\n", "\n", "# ------------ Plot comparación ------------\n", "plt.figure(figsize=(5,4))\n", "plt.plot(phi_list, E_num, 'o', label='|E_num(φ)|')\n", "plt.plot(phi_list, E_analytic_abs, '-', label=r'$E(\\phi) = \\Delta\\sqrt{1 - T\\sin^2(\\phi/2)}$')\n", "plt.xlabel(r'$\\phi$')\n", "plt.ylabel(r'$E(\\phi)$')\n", "##plt.title(f'SNS 1D corta con barrera Vb={Vb:.2f}, T≈{T_normal:.3f}')\n", "##plt.grid(True)\n", "plt.legend()\n", "plt.tight_layout()\n", "plt.show()\n" ] }, { "cell_type": "markdown", "id": "b56ea560", "metadata": {}, "source": [ "### Symmetry Checking" ] }, { "cell_type": "markdown", "id": "50489ef8", "metadata": {}, "source": [ "Remember that when we defined `~kwant.builder.Builder` for the left lead above,\n", "we not only declared an electron-hole conservation law, but also that the Hamiltonian\n", "has the particle-hole symmetry :math:`\\mathcal{P} = \\sigma_y` which anticommutes\n", "with the Hamiltonian, using the argument ``particle_hole``.\n", "In Kwant, whenever one or more of the fundamental discrete symmetries\n", "(time-reversal, particle-hole and chiral) are present in a lead Hamiltonian,\n", "they can be declared in `~kwant.builder.Builder`. Kwant then automatically uses\n", "them to construct scattering states that obey the specified symmetries. In this\n", "example, we have a discrete symmetry declared in addition to a conservation law.\n", "For any two conservation law blocks that are transformed to each other by the\n", "discrete symmetry, Kwant then automatically computes the scattering states of one\n", "block by applying the symmetry operator to the scattering states of the other.\n", "\n", "Now, :math:`\\mathcal{P}` relates electrons and holes\n", "at *opposite* energies. However, a scattering problem is always solved at a\n", "fixed energy, so generally :math:`\\mathcal{P}` does not give a relation between\n", "the electron and hole blocks. The exception is of course at zero energy, in which\n", "case particle-hole symmetry transforms between the electron and hole blocks, resulting\n", "in a symmetric scattering matrix. We can check the symmetry explicitly with" ] }, { "cell_type": "code", "execution_count": 86, "id": "1d6b1f62", "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "s_ee: \n", " [[ 0.538+0.823j 0. +0.j ]\n", " [-0. -0.j 0.515-0.856j]]\n", "s_hh: \n", " [[ 0.538-0.823j 0. -0.j ]\n", " [-0. +0.j 0.515+0.856j]]\n", "s_hh: \n", "\\ no order [[ 0.515+0.856j -0. +0.j ]\n", " [ 0. -0.j 0.538-0.823j]]\n", "s_ee - s_hh^*: \n", " [[ 0.-0.j 0.+0.j]\n", " [-0.+0.j 0.-0.j]] \n", "\n", "s_he: \n", " [[-0.+0.j 0.-0.054j]\n", " [-0.-0.179j 0.-0.j ]]\n", "s_eh: \n", " [[-0.+0.j -0.-0.054j]\n", " [-0.-0.179j 0.-0.j ]]\n", "s_he + s_eh^*: \n", " [[-0.+0.j 0.+0.j]\n", " [-0.-0.j 0.+0.j]]\n" ] } ], "source": [ "#### Cheking the symmetries \n", "\n", "def check_PHS(syst):\n", " # Scattering matrix\n", " s = kwant.smatrix(syst, energy=0)\n", " # Electron to electron block\n", " s_ee = s.submatrix((0,0), (0,0))\n", " # Hole to hole block\n", " s_hh = s.submatrix((0,1), (0,1))\n", " print('s_ee: \\n', np.round(s_ee, 3))\n", " print('s_hh: \\n', np.round(s_hh[::-1, ::-1], 3))\n", " print('s_hh: \\n\\ no order', np.round(s_hh, 3))\n", " print('s_ee - s_hh^*: \\n',\n", " np.round(s_ee - s_hh[::-1, ::-1].conj(), 3), '\\n')\n", " # Electron to hole block\n", " s_he = s.submatrix((0,1), (0,0))\n", " # Hole to electron block\n", " s_eh = s.submatrix((0,0), (0,1))\n", " print('s_he: \\n', np.round(s_he, 3))\n", " print('s_eh: \\n', np.round(s_eh[::-1, ::-1], 3))\n", " print('s_he + s_eh^*: \\n',\n", " np.round(s_he + s_eh[::-1, ::-1].conj(), 3))\n", " \n", " \n", "check_PHS(syst)" ] }, { "cell_type": "markdown", "id": "f03498d1", "metadata": {}, "source": [ "Note that $\\mathcal{P}$ flips the sign of momentum, and for the parameters\n", "we consider here, there are two electron and two hole modes active at zero energy.\n", "We thus reorder the matrix elements of the scattering matrix blocks above,\n", "to ensure that the same matrix elements in the electron and hole blocks relate\n", "scattering states and their particle hole partners." ] }, { "cell_type": "markdown", "id": "0b4af405", "metadata": {}, "source": [ "Please send corrections to jalil@udel.edu" ] }, { "cell_type": "code", "execution_count": null, "id": "a0ee56a2", "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python (qtransport)", "language": "python", "name": "qtransport" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.11.13" } }, "nbformat": 4, "nbformat_minor": 5 }