Notebooks/Efeito Aharonov-Bohm.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "15c5f3ff",
   "metadata": {},
   "source": [
    "# Efeito Aharonov-Bohm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "31e14dc9",
   "metadata": {},
   "source": [
    "- PET - Física\n",
    "- Ex-Petiano: Gabriel Wendell Celestino Rocha\n",
    "- Data: 05 de Maio de 2023"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd0ec7b5",
   "metadata": {},
   "source": [
    "O objetivo deste `Notebook` é apresentar uma material introdutório sobre o efeito Aharonov-Bohm e anéis quânticos, assim como, desenvolver códigos para simulação do efeito Aharonov-Bohm em anéis quânticos. Este efeito quântico é importante conceitualmente porque consiste em três problemas (a existência física de potenciais, a fundamentalidade do princípio da mínima ação e o princípio da localidade) que aparecem na teoria eletromagnética clássica como uma teoria de calibre (*gauge*), a qual antes do advento da Mecânica Quântica era tratado apenas como uma formulação matemática sem consequências físicas (apenas filosóficas). Devido a sua importância, o efeito Aharonov-Bohm foi escolhido pela revista *New Scientist* como umas das *sete maravilhas do mundo quântico*. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24514340",
   "metadata": {},
   "source": [
    "Para uma melhor organização deste `Notebook` como um todo, este foi dividido em **3** seções:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8bc5af64",
   "metadata": {},
   "source": [
    "1. **Efeito Aharonov-Bohm**;\n",
    "2. **Anéis Quânticos**;\n",
    "3. **Simulação de um Anel Quântico**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e98f6e1",
   "metadata": {},
   "source": [
    "## Pré-requisitos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "297efe86",
   "metadata": {},
   "source": [
    "Este `Notebook` assume que o leitor tenha um conhecimento básico de Mecânica Quântica a nível de graduação, uma vez que o assunto aqui abordado geralmente só é apresentado em cursos avançados de pós-graduação em Mecânica Quântica ou em Trabalhos de Conclusão de Curso (TCCs) de estudantes que fazem pesquisa em áreas correlacionadas ou derivadas da Mecânica Quântica. Diante disso, é necessário que o leitor tenha conhecimento da área de Mecânica Quântica no nível apresentado no livro *Modern Quantum Mechanics* de J. J. Sakurai **[1]**. Note que esse `Notebook` serve como uma introdução ao efeito Aharanov-Bohm e como um possível tema a ser explorado em uma iniciação científica (IC)."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "068df2e6",
   "metadata": {},
   "source": [
    "### Importando as bibliotecas"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "63da6f87",
   "metadata": {},
   "outputs": [],
   "source": [
    "from mpl_toolkits.axes_grid1 import make_axes_locatable\n",
    "from numpy.random import default_rng\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import kwant\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "def opt_plot():\n",
    "    # plt.style.use('dark_background')\n",
    "    plt.grid(True, linestyle = ':', color = '0.50')\n",
    "    plt.rcParams['text.usetex'] = True\n",
    "    # plt.rcParams['font.family'] = 'monospace'\n",
    "    plt.rcParams['font.size'] = 15\n",
    "    plt.minorticks_on()\n",
    "    plt.tick_params(axis = 'both', which = 'minor', direction = \"in\",\n",
    "                        top = True, right = True, length = 5, width = 1, labelsize = 15)\n",
    "    plt.tick_params(axis = 'both', which = 'major', direction = \"in\",\n",
    "                        top = True, right = True, length = 8, width = 1, labelsize = 15)\n",
    "    \n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e4c5fbb7",
   "metadata": {},
   "source": [
    "#### Detalhes das bibliotecas:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "463464b7",
   "metadata": {},
   "outputs": [
    {
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         "version": "3.9.8 64bit [MSC v.1929 64 bit (AMD64)]"
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         "version": "1.4.3"
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         "module": "Matplotlib",
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         "module": "Numpy",
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       "{\\bf Software} & {\\bf Version} \\\\ \\hline\\hline\n",
       "Python & 3.9.8 64bit [MSC v.1929 64 bit (AMD64)] \\\\ \\hline\n",
       "IPython & 8.0.1 \\\\ \\hline\n",
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       "Matplotlib & 3.6.0 \\\\ \\hline\n",
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       "Software versions\n",
       "Python 3.9.8 64bit [MSC v.1929 64 bit (AMD64)]\n",
       "IPython 8.0.1\n",
       "OS Windows 10 10.0.19044\n",
       "Kwant 1.4.3\n",
       "Matplotlib 3.6.0\n",
       "Numpy 1.21.6\n",
       "Fri Apr 21 19:30:53 2023 Hora Padrão de Buenos Aires"
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   "source": [
    "%load_ext version_information\n",
    "%version_information Kwant, Matplotlib, Numpy"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "67ed3c77",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "20c23418",
   "metadata": {},
   "source": [
    "## 1. Efeito Aharonov-Bohm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72f2104a",
   "metadata": {},
   "source": [
    "O efeito Aharonov-Bohm é um fenômeno de interferência que demonstra a influência do potencial eletromagnético sobre a fase da função de onda de uma partícula carregada mesmo em uma região onde os campos eletromagnéticos são nulos."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80abf76e",
   "metadata": {},
   "source": [
    "### 1.1 Deslocamento do padrão de interferência devido à presença de um solenóide"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "9c4c8c51",
   "metadata": {},
   "source": [
    "Um solenoide infinito possui um campo magnético nulo em seu exterior, e em seu interior, esse campo é dado por"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c419f211",
   "metadata": {},
   "source": [
    "$$\\tag{1.1}\n",
    "\\boldsymbol{B}=\\frac{4\\pi}{c}\\nu I\\boldsymbol{e}_{z}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce467a99",
   "metadata": {},
   "source": [
    "em que $I$ é a corrente circulando nas espiras do solenoide e $\\nu$ é o número de de espiras por\n",
    "unidade de comprimento."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7554df12",
   "metadata": {},
   "source": [
    "Se $r$ é a distância radial até o centro do solenoide e $\\boldsymbol{e}_{\\phi}$ é o versor azimutal em coordendas polares, e dado um solenoide de raio da seção transversal igual a $R$, o potencial vetor produzido é"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6127bd94",
   "metadata": {},
   "source": [
    "$$\\tag{1.2}\n",
    "\\boldsymbol{A}\\left(\\boldsymbol{r}\\right)=\\begin{cases}\n",
    "\\frac{\\Phi}{2\\pi R^{2}}r\\boldsymbol{e}_{\\phi} & \\text{para }r\\leq R\\quad;\\\\\n",
    "\\frac{\\Phi}{2\\pi}\\frac{1}{r}\\boldsymbol{e}_{\\phi} & \\text{para }r>R\\quad.\n",
    "\\end{cases}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4efac15d",
   "metadata": {},
   "source": [
    "Como os elétrons atravessam uma região em que os campos eletromagnéticos são nulos, não há atuação da força de Lorentz sobre eles. Todavia, a localização dos máximos do padrão de interferência dos elétrons depende do campo magnético confinado ao solenóide, conforme mostrado na equação"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2787f8dd",
   "metadata": {},
   "source": [
    "$$\\tag{1.3}\n",
    "Y_{n}=Y'_{n}+\\frac{L\\tilde{\\lambda}}{d}\\frac{e}{c\\hbar}\\Phi\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "470646df",
   "metadata": {},
   "source": [
    "O fenômeno descrito nesta seção, em que o potencial altera a fase da função de onda, é o efeito Aharonov-Bohm, o qual foi previsto por Yakir Aharonov e David Bohm em 1959 [(**AHARONOV; BOHM, 1959**)](https://journals.aps.org/pr/abstract/10.1103/PhysRev.115.485) **[2]**. A primeira comprovação experimental foi publicada no ano seguinte [(**CHAMBERS, 1960**)](https://link.aps.org/doi/10.1103/PhysRevLett.5.3) **[3]**. Também é possível obter o efeito de alteração da fase da função de onda via fluxo elétrico [(**BROMLEY; GREINER, 2012**)](https://books.google.com.br/books?id=Ei7vCAAAQBAJ) **[4]**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c02ff8fd",
   "metadata": {},
   "source": [
    "### 1.2 Incorporação de Efeitos Macroscópicos ao Efeito Aharonov-Bohm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b2b379c4",
   "metadata": {},
   "source": [
    "O desvio de fase que resulta no deslocamento dos máximos do padrão de interferência, mostrado em $(1.3)$, não é devido à força de Lorentz, haja vista o campo elétrico ser nulo na região atravessada pelo elétron, estando o campo magnético confinado ao interior do solenoide."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80d7d806",
   "metadata": {},
   "source": [
    "O efeito macroscópico de deslocamento do padrão de interferência também pode ser calculado pela equação $(1.3)$. A figura abaixo ilustra o caso em que o campo magnético de intensidade B não está confinado ao interior de um solenoide, fazendo com que uma força de Lorentz de módulo $F=\\left(e/c\\right)vB$ atue sobre um elétron com velocidade $v$. Se essa força for aplicada ao elétron por um tempo $\\tau$, o momento linear produzido será de $p_{y}=\\tau F=\\tau(e/c)vB$, com ângulo de deflexão $\\tan\\left(\\theta\\right)=p_{y}/p=\\Delta Y/L$, resultando em"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52580d3c",
   "metadata": {},
   "source": [
    "$$\\tag{1.4}\n",
    "\\Delta Y=L\\frac{p_{y}}{p}=DL\\frac{eB}{pc}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "985944f4",
   "metadata": {},
   "source": [
    "Observando a figura abaixo, nota-se que o fluxo magnético $\\Phi$ é dado pela relação abaixo. Substituindo $\\Phi$ em $(1.3)$ obtemos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cd979879",
   "metadata": {},
   "source": [
    "$$\\tag{1.5}\n",
    "\\Phi=\\oint\\text{d}\\boldsymbol{S}\\cdot\\boldsymbol{B}=BDd\\quad\\therefore\\quad \\boxed{Y=\\frac{L\\tilde{\\lambda}}{d}\\frac{e}{c\\hbar}\\Phi=DL\\frac{eB}{pc}}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6764fbc1",
   "metadata": {},
   "source": [
    "$\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60796c21",
   "metadata": {},
   "source": [
    "Esse resultado está de acordo com o previsto pela equação $(1.4)$. Isso corrobora o fato de que o efeito macroscópico de deslocamento do padrão de interferência também pode ser calculado pela equação $(1.3)$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4311cecd",
   "metadata": {},
   "source": [
    "![Figura 1](img/Aharanov-Bohm/img1.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "83e2fc27",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b1da2b48",
   "metadata": {},
   "source": [
    "## 2. Anéis Quânticos"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fc6d9948",
   "metadata": {},
   "source": [
    "Nesse capítulo será estudada a aparência da fase de Aharonov-Bohm para o caso em que um elétron tem o seu movimento restrito a um caminho circular ao redor de um fluxo magnético. Apresentações mais detalhadas dos tópicos abordados nesse capítulo podem ser encontradas em [(**IHN, 2010**)](https://books.google.com.br/books?id=UdgVDAAAQBAJ) **[5]** e [(**NAZAROV; BLANTER, 2009**)](https://books.google.com.br/books?id=bjmXJOFmqZIC) **[6]**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "089538f1",
   "metadata": {},
   "source": [
    "### 2.1 Transmissão em um Anel Aberto"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0baaeaad",
   "metadata": {},
   "source": [
    "O hamiltoniano que descreve o movimento de uma carga $e$ que interage com um potencial vetor $\\boldsymbol{A}$ é"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "233116c3",
   "metadata": {},
   "source": [
    "$$\\tag{2.1}\n",
    "\\hat{H}=\\frac{1}{2m}\\left(\\hat{p}-\\frac{e}{c}\\boldsymbol{A}\\right)^{2}+V\\left(r\\right)\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2c4460ed",
   "metadata": {},
   "source": [
    "A uma distância $r$ do centro do anel (em que o fluxo está confinado), o potencial vetor é dado por"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "72b73347",
   "metadata": {},
   "source": [
    "$$\\tag{2.2}\n",
    "\\boldsymbol{A}=\\frac{\\phi}{2\\pi r}\\boldsymbol{e}_{\\varphi}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ac35ba35",
   "metadata": {},
   "source": [
    "O _quantum_ de fluxo magnético é dado por"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "756013fd",
   "metadata": {},
   "source": [
    "$$\n",
    "\\phi_{0}=\\frac{hc}{e}=\\frac{2\\pi hc}{2\\pi e}=\\frac{2\\pi\\hbar c}{e}\\implies \\boldsymbol{A}=\\frac{\\phi}{2\\pi r}\\boldsymbol{e}_{\\varphi}=\\frac{\\frac{2\\pi\\hbar c}{e}}{\\phi_{0}}\\frac{\\phi}{2\\pi r}\\boldsymbol{e}_{\\varphi}=\\frac{\\hbar c}{e}\\frac{\\phi}{\\phi_{0}}\\frac{1}{r}\\boldsymbol{e}_{\\varphi}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5bf58966",
   "metadata": {},
   "source": [
    "$$\\tag{2.3}\n",
    "\\therefore\\quad\\hat{H}=\\frac{1}{2m}\\left(-i\\hbar\\nabla-\\frac{e}{c}\\frac{\\hbar c}{e}\\frac{\\phi}{\\phi_{0}}\\frac{1}{r}\\boldsymbol{e}_{\\varphi}\\right)^{2}+V\\left(r\\right)\\text{ }.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "77089c3d",
   "metadata": {},
   "source": [
    "Se o movimento do elétron estiver restrito à circunferência de raio $r=r_0$ no plano $z=0$, então $\\nabla = \\hat{e}_{r}\\left(\\partial/\\partial r\\right) + \\hat{e}_{\\varphi}\\left(1/r\\right)\\partial/\\partial\\varphi + \\hat{e}_{z}\\left(\\partial/\\partial z\\right)$ resume-se ao operador $\\left(1/r\\right)\\partial/\\partial\\varphi$, portanto,"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce0b456b",
   "metadata": {},
   "source": [
    "$$\\tag{2.4}\n",
    "\\hat{H}=\\frac{1}{2m}\\left(-i\\hbar\\frac{1}{r_{0}}\\frac{\\partial}{\\partial\\varphi}-\\frac{e}{c}\\frac{\\hbar c}{e}\\frac{\\phi}{\\phi_{0}}\\frac{1}{r_{0}}\\right)^{2}=\\frac{\\hbar^{2}}{2mr_{0}^{2}}\\left(-i\\frac{\\partial}{\\partial\\varphi}-\\frac{\\phi}{\\phi_{0}}\\right)^{2}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "94c34499",
   "metadata": {},
   "source": [
    "com $V\\left(r_0\\right)=0$. A solução da equação de autovalores $\\hat{H}\\Psi=E\\Psi$ pode ser dada por $\\Psi_{\\ell}=e^{i\\ell\\varphi}$. Substituindo $\\Psi_{\\ell}$ em $(2.4)$ chega-se a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "fad78931",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left(-i\\frac{\\partial}{\\partial\\varphi}-\\frac{\\phi}{\\phi_{0}}\\right)e^{i\\ell\\varphi}=-i\\frac{\\partial}{\\partial\\varphi}e^{i\\ell\\varphi}-\\frac{\\phi}{\\phi_{0}}e^{i\\ell\\varphi}=\\ell e^{i\\ell\\varphi}-\\frac{\\phi}{\\phi_{0}}e^{i\\ell\\varphi}=\\left(\\ell-\\frac{\\phi}{\\phi_{0}}\\right)\\Psi_{\\ell}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ff507bd1",
   "metadata": {},
   "source": [
    "$$\n",
    "\\left(-i\\frac{\\partial}{\\partial\\varphi}-\\frac{\\phi}{\\phi_{0}}\\right)^{2}\\Psi_{\\ell}=\\left(\\ell-\\frac{\\phi}{\\phi_{0}}\\right)^{2}\\Psi_{\\ell}\\implies\\hat{H}\\Psi_{\\ell}=\\frac{\\hbar^{2}}{2mr_{0}^{2}}\\left(\\ell-\\frac{\\phi}{\\phi_{0}}\\right)^{2}\\Psi_{\\ell}=E_{\\ell}\\Psi_{\\ell}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "97bd9e86",
   "metadata": {},
   "source": [
    "$$\\tag{2.5}\n",
    "\\implies\\ell-\\frac{\\phi}{\\phi_{0}}=\\pm\\sqrt{\\frac{2mr_{0}^{2}}{\\hbar^{2}}E_{\\ell}}\\implies\\ell=\\pm\\sqrt{\\frac{2mE_{\\ell}}{\\hbar^{2}}r_{0}^{2}}+\\frac{\\phi}{\\phi_{0}}\\quad\\therefore\\quad\\boxed{\\ell=\\pm kr_{0}+\\frac{\\phi}{\\phi_{0}}}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd751335",
   "metadata": {},
   "source": [
    "onde $k=\\sqrt{2mE_{\\ell}}/\\hbar$ é o número de onda. Há dois estados possíveis para o elétron, que correspondem a circular o anel em sentido horário ou anti-horário, conforme ilustrado na figura abaixo:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60b71040",
   "metadata": {},
   "source": [
    "![Figura 2](img/Aharanov-Bohm/img2.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "69cb036f",
   "metadata": {},
   "source": [
    "O terminal de entrada pode ser modelado com fase $\\varphi=0$. O elétron pode chegar ao terminal de saída percorrendo o anel em sentido horário até a fase $\\varphi=\\pi$ ou em sentido anti-horário até a fase $\\varphi=−\\pi$. Dessa forma, a função de onda que descreve o elétron transmitido é"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "07349eed",
   "metadata": {},
   "source": [
    "$$\\tag{2.6}\n",
    "\\Psi=\\left[\\frac{1}{\\sqrt{2}}e^{i\\left(kr_{0}+\\frac{\\phi}{\\phi_{0}}\\right)\\pi}+\\frac{1}{\\sqrt{2}}e^{i\\left(-kr_{0}+\\frac{\\phi}{\\phi_{0}}\\right)\\left(-\\pi\\right)}\\right]\\frac{1}{\\sqrt{2}}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e8ffd0b",
   "metadata": {},
   "source": [
    "onde um dos fatores $1/\\sqrt{2}$ é devido a entrada do elétron no anel e o outro fator $1/\\sqrt{2}$ é devido a saída. Dessa forma, a transmissão $T$ é dada por"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "315d27ed",
   "metadata": {},
   "source": [
    "$$\n",
    "T=\\left|\\Psi\\right|^{2}=\\frac{1}{4}\\left|e^{i\\left(kr_{0}+\\frac{\\phi}{\\phi_{0}}\\right)\\pi}+e^{i\\left(-kr_{0}+\\frac{\\phi}{\\phi_{0}}\\right)\\left(-\\pi\\right)}\\right|^{2}=\\frac{\\left|e^{i\\left(kr_{0}\\pi\\right)}\\right|^{2}}{4}\\cdot\\left[2\\cos\\left(\\frac{\\phi}{\\phi_{0}}\\pi\\right)\\right]^{2}\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5b819619",
   "metadata": {},
   "source": [
    "$$\\tag{2.7}\n",
    "\\implies T=\\cos^{2}\\left(\\frac{\\phi}{\\phi_{0}}\\pi\\right)=\\frac{1}{2}+\\frac{1}{2}\\cos\\left(\\frac{\\phi}{\\phi_{0}}2\\pi\\right)\\quad\\therefore\\quad\\boxed{T=\\frac{1}{2}\\left[1+\\cos\\left(\\frac{\\phi}{\\phi_{0}}2\\pi\\right)\\right]}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "439e073d",
   "metadata": {},
   "source": [
    "$\\blacksquare$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "88cd1562",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "ratio_phi = np.linspace(0, 4, 1000)\n",
    "T = 0.5 + 0.5*np.cos(ratio_phi*2*np.pi)\n",
    "\n",
    "\n",
    "plt.figure(figsize = (8,5))\n",
    "plt.plot(ratio_phi, T, color = 'indigo', label = r'$T=\\frac{1}{2}+\\frac{1}{2}\\cos\\left(\\frac{\\phi}{\\phi_{0}}\\cdot2\\pi\\right)$')\n",
    "plt.title('Transmissão em um Anel Quântico')\n",
    "plt.xlabel(r'$\\phi/\\phi_0$')\n",
    "plt.ylabel(r'$T$')\n",
    "\n",
    "plt.legend(loc = 'best')\n",
    "opt_plot()\n",
    "plt.savefig('Transmissão_Anel-Quântico.png', dpi = 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3170aaaa",
   "metadata": {},
   "source": [
    "A transmissão possui também um termo independente do fluxo, associado com probabilidades clássicas de reflexão (elétrons refletidos na entrada do anel). Há ainda um outro termo da transmissão, associado com as oscilações *Altshuler-Aronov-Spivak* (elétrons refletidos após circular completamente o anel). As oscilações de efeito Aharonov-Bohm acentuam-se com a redução da temperatura, e geralmente não são observadas à temperatura ambiente."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d5f717c",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0a6924a",
   "metadata": {},
   "source": [
    "## 3. Simulação de um Anel Quântico"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ade62521",
   "metadata": {},
   "source": [
    "Nesta seção vamos simular um anel quântico utilizando o módulo `kwant` da linguagem Python. O objetivo dessa seção não é descrever os métodos que serviram de base para a criação do pacote `kwant`, porém, será necessário apresentar alguns poucos conhecimentos sobre modelos de ligações fortes e representação matricial do Hamiltoniano. Na primeira seção é apresentado o caso unidimensional. Na segunda seção é apresentado o caso bidimensional. Finalmente, na última seção, é apresentada a descrição detalhada do código Python utilizado na simulação do anel quântico, sendo obtida a curva de condutância em função do fluxo magnético."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "24af6f37",
   "metadata": {},
   "source": [
    "### 3.1  Representação Matricial do Hamiltoniano"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "334d0049",
   "metadata": {},
   "source": [
    "A figura abaixo, ilustra uma cadeia unidimensional formada por cinco sítios atômicos, com índices $i$ variando de $0$ a $4$."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d250f2b5",
   "metadata": {},
   "source": [
    "![Figura 3](img/Aharanov-Bohm/img3.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91fa0cb8",
   "metadata": {},
   "source": [
    "Para uma cadeia unidimensional com constante de rede $a$, a discretização do Hamiltoniano $H$ da equação de Schrödinger será,"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d92d3b2",
   "metadata": {},
   "source": [
    "$$\\tag{3.1}\n",
    "E\\Psi=\\left(-\\frac{\\hbar^{2}}{2m}\\frac{\\text{d}^{2}}{\\text{d}x^{2}}+U\\right)\\Psi=\\hat{H}\\Psi\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "53533559",
   "metadata": {},
   "source": [
    "utilizando uma diferença finita centrada, resulta em:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d6da5fec",
   "metadata": {},
   "source": [
    "$$\\tag{3.2}\n",
    "E\\Psi_{i}=-\\frac{\\hbar^{2}}{2m}\\frac{\\Psi_{i+1}+\\Psi_{i-1}-2\\Psi_{i}}{a^{2}}+U\\Psi_{i}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "dd025688",
   "metadata": {},
   "source": [
    "Fazendo $t=\\frac{\\hbar^{2}}{2ma^{2}}$, e $U=0$, tem-se"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5f773965",
   "metadata": {},
   "source": [
    "$$\\tag{3.3}\n",
    "E\\Psi_{i}=-t\\Psi_{i-1}+2t\\Psi_{i}-t\\Psi_{i+1}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7ab1d5d6",
   "metadata": {},
   "source": [
    "Para o caso da cadeia mostrada na figura acima, chega-se as expressões"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46399811",
   "metadata": {},
   "source": [
    "\\begin{cases}\\tag{3.4}\n",
    "E\\Psi_{0}= & -t\\Psi_{-1}+2t\\Psi_{0}-t\\Psi_{1}\\quad,\\\\\n",
    "E\\Psi_{1}= & -t\\Psi_{0}+2t\\Psi_{1}-t\\Psi_{2}\\quad,\\\\\n",
    "E\\Psi_{2}= & -t\\Psi_{1}+2t\\Psi_{2}-t\\Psi_{3}\\quad,\\\\\n",
    "E\\Psi_{3}= & -t\\Psi_{2}+2t\\Psi_{3}-t\\Psi_{4}\\quad,\\\\\n",
    "E\\Psi_{4}= & -t\\Psi_{3}+2t\\Psi_{4}-t\\Psi_{5}\\quad.\n",
    "\\end{cases}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4d344e4b",
   "metadata": {},
   "source": [
    "Utilizando as condições de contorno $\\Psi_{i}\\left(-1\\right)=\\Psi_{i}\\left(5\\right)=0$, obtém-se a matriz Hamiltoniana"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc34717b",
   "metadata": {},
   "source": [
    "$$\\tag{3.5}\n",
    "H=\\left(\\begin{array}{ccccc}\n",
    "2t & -t & 0 & 0 & 0\\\\\n",
    "-t & 2t & -t & 0 & 0\\\\\n",
    "0 & -t & 2t & -t & 0\\\\\n",
    "0 & 0 & -t & 2t & -t\\\\\n",
    "0 & 0 & 0 & -t & 2t\n",
    "\\end{array}\\right)\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7247b9cd",
   "metadata": {},
   "source": [
    "$\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ba89b4d4",
   "metadata": {},
   "source": [
    "### 3.2 Modelo de Ligações Fortes"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c800167e",
   "metadata": {},
   "source": [
    "Uma rede de Bravais bidimensional é o conjunto de pontos que possuem vetores posição $\\boldsymbol{R}$ da forma"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8e51839c",
   "metadata": {},
   "source": [
    "$$\\tag{3.6}\n",
    "\\boldsymbol{R}=n_{x}\\boldsymbol{a}_{x}+n_{y}\\boldsymbol{a}_{y}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a1bd3b6a",
   "metadata": {},
   "source": [
    "em que $\\boldsymbol{a}_{x}$ e $\\boldsymbol{a}_{y}$ são vetores no plano da rede e $n_{x},n_{y}\\in\\mathbb{Z}$. Na figura abaixo, é mostrada uma rede de Bravais quadrada."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0860a0a1",
   "metadata": {},
   "source": [
    "Os pontos da rede de Bravais podem ser preenchidos com um mesmo conjunto de átomos, denominado de base. Uma rede de Bravais com uma base forma uma estrutura cristalina, que caracteriza os sólidos cristalinos."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8f1c49e2",
   "metadata": {},
   "source": [
    "A periodicidade da rede de Bravais quadrada com $\\boldsymbol{R}=n_{x}\\boldsymbol{a}_{x}+n_{y}\\boldsymbol{a}_{y}$ mostrada na figura abaixo resulta na periodicidade do potencial $U\\left(\\boldsymbol{r}\\right)$, dado por"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "80689d74",
   "metadata": {},
   "source": [
    "$$\\tag{3.7}\n",
    "U\\left(\\boldsymbol{r}\\right)=U\\left(\\boldsymbol{r}+\\boldsymbol{R}\\right)\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5a09e005",
   "metadata": {},
   "source": [
    "![Figura 4](img/Aharanov-Bohm/img4.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "009146bc",
   "metadata": {},
   "source": [
    "O teorema de Bloch afirma que num potencial periódico a função de onda $\\psi_{\\boldsymbol{k}}\\left(\\boldsymbol{r}\\right)$de um elétron independente, que não interage com os demais elétrons, é dada pelo produto de uma onda plana por uma função periódica da rede $u_{\\boldsymbol{k}}\\left(\\boldsymbol{k}\\right)$, isto é,"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7fdac8e1",
   "metadata": {},
   "source": [
    "$$\\tag{3.8}\n",
    "\\psi_{\\boldsymbol{k}}\\left(\\boldsymbol{r}\\right)=\\exp\\left(i\\boldsymbol{k}\\cdot\\boldsymbol{r}\\right)\\cdot u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}\\right),\\quad\\text{com:}\\quad u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}\\right)=u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}+\\boldsymbol{R}\\right)\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "442698f5",
   "metadata": {},
   "source": [
    "Levando em conta a interação entre os elétrons, a função de onda $\\Psi\\left(\\boldsymbol{r}\\right)$ de um elétron em qualquer ponto da rede pode ser obtida através da **combinação linear de orbitais atômicos** ou LCAO (*Linear Combinations of Atomic Orbitals*), sendo expressa como"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "1b86dae4",
   "metadata": {},
   "source": [
    "$$\\tag{3.9}\n",
    "\\Psi_{\\boldsymbol{k}}\\left(\\boldsymbol{r}\\right)=\\sum_{m}c_{m}\\cdot\\psi_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)=\\frac{1}{\\sqrt{N}}\\sum_{m}\\exp\\left(i\\boldsymbol{k}\\cdot\\boldsymbol{r}_{m}\\right)\\cdot u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)=\\sum_{m}C_{m}\\cdot u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)\\quad\\therefore\\quad C_{m}=\\frac{1}{\\sqrt{N}}\\cdot\\exp\\left(i\\boldsymbol{k}\\cdot\\boldsymbol{r}_{m}\\right)\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6b841b8",
   "metadata": {},
   "source": [
    "onde $\\boldsymbol{r}_{m}$ é a posição do $m$-ésimo átomo e $N$ é o número total de sítios atômicos (pontos da rede de Bravais quadrada contendo um único átomo). Resolvendo a equação de Schrödinger independente do tempo para $(3.8)$, tem-se"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "79f67b28",
   "metadata": {},
   "source": [
    "$$\n",
    "H\\Psi_{\\boldsymbol{k}}=E\\Psi_{\\boldsymbol{k}}\\iff u^{*}_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{n}\\right)H\\Psi_{\\boldsymbol{k}}=u^{*}_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{n}\\right)E\\Psi_{\\boldsymbol{k}}=E u^{*}_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{n}\\right)\\Psi_{\\boldsymbol{k}}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "016fa444",
   "metadata": {},
   "source": [
    "$$\\tag{3.10}\n",
    "\\implies u_{\\boldsymbol{k}}^{*}\\left(\\boldsymbol{r}_{n}\\right)H\\sum_{m}C_{m}u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)=Eu_{\\boldsymbol{k}}^{*}\\left(\\boldsymbol{r}_{n}\\right)\\left[\\sum_{m}C_{m}u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)\\right]\\quad \\therefore \\quad \\sum_{m}u_{\\boldsymbol{k}}^{*}\\left(\\boldsymbol{r}_{n}\\right)Hu_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)C_{m}=E\\sum_{m}u_{\\boldsymbol{k}}^{*}\\left(\\boldsymbol{r}_{n}\\right)u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)C_{m}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e070e88b",
   "metadata": {},
   "source": [
    "Integrando a equação anterior em todo o espaço e definindo"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "767ddf2b",
   "metadata": {},
   "source": [
    "$$\n",
    "\\begin{cases}\\tag{3.11}\n",
    "H_{nm} = & \\int u_{\\boldsymbol{k}}^{*}\\left(\\boldsymbol{r}_{n}\\right)Hu_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)\\text{d}\\boldsymbol{r}\\quad,\\\\\n",
    "S_{nm} = & \\int u_{\\boldsymbol{k}}^{*}\\left(\\boldsymbol{r}_{n}\\right)u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)\\text{d}\\boldsymbol{r}\\quad, \n",
    "\\end{cases}\n",
    "\\implies\\sum_{m}H_{nm}C_{m}=E\\sum_{m}S_{nm}C_{m}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c1c17a0b",
   "metadata": {},
   "source": [
    "Da definição de $S_{nm}$, vê-se que, se $u_{\\boldsymbol{k}}\\left(\\boldsymbol{r}_{m}\\right)$ for ortonormal, então $S_{nm}=1$ para $n=m$ e $S_{nm}=0$ para $n\\neq m$, portanto,"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc79cf90",
   "metadata": {},
   "source": [
    "$$\\tag{3.12}\n",
    "EC_{n}=\\sum_{m}H_{nm}C_{m}\\implies E=\\sum_{m}H_{nm}\\frac{C_{m}}{C_{n}}\\implies E=\\sum_{m}H_{nm}\\frac{\\frac{1}{\\sqrt{N}}\\cdot e^{\\left(i\\boldsymbol{k}\\cdot\\boldsymbol{r}_{m}\\right)}}{\\frac{1}{\\sqrt{N}}\\cdot e^{\\left(i\\boldsymbol{k}\\cdot\\boldsymbol{r}_{n}\\right)}}\\quad\\therefore\\quad\\boxed{E\\left(\\boldsymbol{k}\\right)=\\sum_{m}H_{nm}\\cdot\\exp\\left[i\\boldsymbol{k}\\cdot\\left(\\boldsymbol{r}_{m}-\\boldsymbol{r}_{n}\\right)\\right]}\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0487950d",
   "metadata": {},
   "source": [
    "$\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "12795e55",
   "metadata": {},
   "source": [
    "que é a relação de dispersão para um elétron na rede cristalina."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "8da42874",
   "metadata": {},
   "source": [
    "Para uma constante de rede $||\\boldsymbol{a}_{x}||=||\\boldsymbol{a}_{y}||=a$, utilizando um modelo de ligações fortes (*tight binding*), em que $\\varepsilon$ é o elemento da matriz Hamiltoniana correspondente ao sítio atômico e $−t$ é o elemento de salto (*hopping*) entre átomos que são primeiros vizinhos, conforme ilustrado na figura abaixo, tem-se $H_{mm}=\\varepsilon$, $H_{nm}=−t$ para $\\boldsymbol{r}_{m}−\\boldsymbol{r}_{n}=\\boldsymbol{a}_{x}$, $\\boldsymbol{r}_{m}−\\boldsymbol{r}_{n}=\\boldsymbol{a}_{y}$, $\\boldsymbol{r}_{m}−\\boldsymbol{r}_{n}=−\\boldsymbol{a}_{x}$, $\\boldsymbol{r}_{m}−\\boldsymbol{r}_{n}=−\\boldsymbol{a}_{y}$, e $H_{nm}=0$ para outros valores de $\\boldsymbol{r}_{m}−\\boldsymbol{r}_{n}$. Daí resulta que"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "594ab294",
   "metadata": {},
   "source": [
    "$$\\tag{3.13}\n",
    "E\\left(\\boldsymbol{k}\\right)=\\varepsilon-t\\cdot e^{ik_{x}a}-t\\cdot e^{ik_{y}a}-t\\cdot e^{-ik_{x}a}-t\\cdot e^{-ik_{y}a}\\quad\\therefore\\quad \\boxed{E\\left(\\boldsymbol{k}\\right)=\\varepsilon-2t\\cos\\left(k_{x}a\\right)-2t\\cos\\left(k_{y}a\\right)}\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "54d84aff",
   "metadata": {},
   "source": [
    "Se $E\\left(0\\right)=0$, temos então"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d35861da",
   "metadata": {},
   "source": [
    "$$\\tag{3.14}\n",
    "E\\left(0\\right)=\\varepsilon-2t-2t=\\varepsilon-4t=0\\implies\\varepsilon=4t\\quad.\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "71756784",
   "metadata": {},
   "source": [
    "Dessa forma, se a matriz hamiltoniana $H$ for discretizada nos sítios atômicos identificados pelas coordenadas espaciais inteiras $\\left(i,j\\right)$ de uma rede com constante de rede $a$, então"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "19ce44f9",
   "metadata": {},
   "source": [
    "\\begin{cases}\\tag{3.15}\n",
    "H_{n_{\\left(i,j\\right)}m_{\\left(i,j\\right)}} = & 4t\\quad,\\\\\n",
    "H_{n_{\\left(i,j\\right)}m_{\\left(i,j-1\\right)}} = & H_{n_{\\left(i,j\\right)}m_{\\left(i-1,j\\right)}}=-t\\quad.\n",
    "\\end{cases}"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6b2360d6",
   "metadata": {},
   "source": [
    "![Figura 5](img/Aharanov-Bohm/img5.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2f936451",
   "metadata": {},
   "source": [
    "$\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f6ab9e9c",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "52909198",
   "metadata": {},
   "source": [
    "### 3.3 Simulação do Efeito Aharonov-Bohm"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f4ef17ba",
   "metadata": {},
   "source": [
    "O efeito Aharonov-Bohm em um anel condutor pode ser simulado através de um script escrito em linguagem python com o pacote [`kwant`](https://kwant-project.org/doc/1/). "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cc5865b7",
   "metadata": {},
   "source": [
    "Primeiro, criamos a matriz Hamitoniana da região de espalhamento através do construtor [`Builder()`](https://kwant-project.org/doc/1/reference/generated/kwant.builder.Builder) do módulo `kwant`. Em seguida, utilizamos o método [`lattice.square()`](https://kwant-project.org/doc/1.0/reference/generated/kwant.lattice.square) para criar uma rede quadrada. Nesse método devemos fornecer como argumento a constante da rede $a$. Aqui, vamos definir uma rede quadrada com constante de rede unitária, ou seja, $a=1$:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "4842e2f4",
   "metadata": {},
   "outputs": [],
   "source": [
    "H = kwant.Builder()\n",
    "\n",
    "a = 1\n",
    "lattice = kwant.lattice.square(a)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "154557a9",
   "metadata": {},
   "source": [
    "Vamos utilizar um sistema de unidades tal que $t=\\hbar^{2}/2ma^{2}$ para definir o raio externo do anel, o raio interno do anel e a largura de contato, respectivamente:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "8d79cf89",
   "metadata": {},
   "outputs": [],
   "source": [
    "t = 1.0\n",
    "r_ext = 20*a\n",
    "r_int = 10*a\n",
    "cont_width = 8*a"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c6b6e7ad",
   "metadata": {},
   "source": [
    "A matriz Hamiltoniana é definida de maneira que $\\varepsilon=4t$ e o elemento de salto entre átomos que são primeiros vizinhos seja $−t$. Para isso, são criados dois laços do tipo `for` que varrem todos os pontos da rede, os quais foram aqui identificados como `lattice(i, j)`. Para preencher a matriz Hamiltoniana, atribui-se diretamente seus valores ao array `H` criado, utilizando como índices o sítio atômico `[lattice(i, j)]`, para o elemento no sítio, e `[lattice(i1, j1), lattice(i2, j2)]`, para o potencial de salto entre primeiros vizinhos. A matriz Hamiltoniana da região de espalhamento é definida como:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "6c119738",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(2*r_ext):\n",
    "    for j in range(2*r_ext):\n",
    "        if ((i - r_ext)**2+(j - r_ext)**2 > (r_int)**2) \\\n",
    "            and ((i - r_ext)**2 + (j - r_ext)**2<(r_ext)**2):\n",
    "            H[lattice(i - r_ext, j - r_ext)] = 4 * t\n",
    "            \n",
    "            if ((i - r_ext)**2 + (j-1 - r_ext)**2 > (r_int)**2) \\\n",
    "                and ((i - r_ext)**2 + (j-1 - r_ext)**2 < (r_ext)**2):\n",
    "                H[lattice(i - r_ext,j - r_ext), lattice(i - r_ext, j\\\n",
    "                    - r_ext - 1)] = -t\n",
    "                \n",
    "            if ((i-1 - r_ext)**2 + (j - r_ext)**2 > (r_int)**2) \\\n",
    "                and ((i-1  -r_ext)**2+(j - r_ext)**2 < (r_ext)**2):\n",
    "                    H[lattice(i - r_ext, j - r_ext), lattice(i - r_ext-1, j\\\n",
    "                        - r_ext)] = -t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b09146de",
   "metadata": {},
   "source": [
    "Os elétrons são modelados como ondas planas que entram na região de espalhamento através de um contato semi-infinito, e saem dela por outro contato semi-infinito. Para definir o Hamiltoniano de um contato, utiliza-se o construtor `Builder()`, cujo argumento deve ser um objeto que define a simetria do contato, criado pelo construtor [`TranslationalSymmetry()`](https://kwant-project.org/doc/1/reference/generated/kwant.lattice.TranslationalSymmetry), que pode ter como argumento um vetor $\\boldsymbol{v}$, indicando o módulo e o sentido da translação espacial em que o contato será infinitamente estendido. O vetor $\\boldsymbol{v}$ deve ser $(−a,0)$ e $(a, 0)$, respectivamente, nos contatos esquerdo e direito. Os contatos são então construídos:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "2c0f07ae",
   "metadata": {},
   "outputs": [],
   "source": [
    "left_cont_symmetry = kwant.TranslationalSymmetry((-a, 0))\n",
    "left_cont_H = kwant.Builder(left_cont_symmetry)\n",
    "\n",
    "right_cont_symmetry = kwant.TranslationalSymmetry((a, 0))\n",
    "right_cont_H = kwant.Builder(right_cont_symmetry)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "876b5dc2",
   "metadata": {},
   "source": [
    "Os Hamiltonianos dos contatos são preenchidos da seguinte forma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "3a11e551",
   "metadata": {},
   "outputs": [],
   "source": [
    "for j in range(2*r_ext):\n",
    "    if j >= r_ext - cont_width/2 \\\n",
    "        and j <= r_ext + cont_width/2:\n",
    "        left_cont_H[lattice(0 - r_ext, j - r_ext)] = 4*t\n",
    "        left_cont_H\\\n",
    "            [lattice(1 - r_ext, j - r_ext), lattice(0 - r_ext, j\\\n",
    "                - r_ext)] = -t\n",
    "        if j > r_ext - cont_width/2:\n",
    "            left_cont_H\\\n",
    "                [lattice(0 - r_ext, j - r_ext), lattice(0 - r_ext, j - 1\\\n",
    "                    - r_ext)] = -t\n",
    "            \n",
    "    for j in range(2*r_ext):\n",
    "        if j >= r_ext - cont_width/2 \\\n",
    "            and j <= r_ext + cont_width/2:\n",
    "            right_cont_H[lattice(0 - r_ext, j - r_ext)] = 4*t\n",
    "            right_cont_H\\\n",
    "                [lattice(2*r_ext+1 - r_ext, j - r_ext), lattice(2*r_ext\\\n",
    "                    - r_ext, j - r_ext)] = -t\n",
    "            if j > r_ext - cont_width/2:\n",
    "                right_cont_H\\\n",
    "                    [lattice(2*r_ext - r_ext, j - r_ext), \\\n",
    "                        lattice(2*r_ext - r_ext, j-1 - r_ext)] = -t"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d73dcaf4",
   "metadata": {},
   "source": [
    "O método `attach_lead()` tem a função de anexar um contato ao objeto da classe `Builder()`. Os Hamiltonianos dos contatos foram anexados ao Hamiltoniano do sistema. O método `plot()` do pacote `kwant` plota o modelo da estrutura que está sendo simulada. A seu turno, esse método utiliza o método `pyplot` do módulo `matplotlib`, sendo necessário, portanto, importá-lo para o programa. Para visualizar o sistema, escrevemos o seguinte:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "f284d9d1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "H.attach_lead(left_cont_H)\n",
    "H.attach_lead(right_cont_H)\n",
    "\n",
    "kwant.plotter.plot(H, site_color = 'black')"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "68ba9b61",
   "metadata": {},
   "source": [
    "Criamos um array `conductance`, inicializado com valores iguais a zero. Criamos também um array `phi`, inicializando com os valores dos fluxos magnéticos no interior do anel em unidades $h/e$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a0ecb1cf",
   "metadata": {},
   "outputs": [],
   "source": [
    "conductance = [0 for i in range(200)]\n",
    "phi = [4.0*0.005*i for i in range(200)]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a3297bb",
   "metadata": {},
   "source": [
    "Em virtude da simetria do anel quântico, tem-se $\\Psi\\left(\\theta+2\\pi\\right)=\\Psi\\left(\\theta\\right)$. No entanto, o efeito do fluxo $\\phi_{B}$ é o de criar uma diferença de fase de Aharonov-Bohm igual a $2\\pi\\left(\\phi_{B}/\\phi_{0}\\right)$:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0ec4b97d",
   "metadata": {},
   "source": [
    "$$\\tag{3.16}\n",
    "\\Psi\\left(\\theta+2\\pi\\right)=\\exp{\\left(i\\cdot 2\\pi\\frac{\\phi_B}{\\phi_0}\\right)}\\cdot\\Psi\\left(\\theta\\right)\\quad,\n",
    "$$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "c384969d",
   "metadata": {},
   "source": [
    "satisfazendo uma condição de contorno torcida, a qual está associada a um ramo de corte, como ilustrado na figura abaixo retirada de ([**SANTOS; WANG, 2014**](https://link.aps.org/doi/10.1103/PhysRevB.89.195122)) **[7]**."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3c9c9611",
   "metadata": {},
   "source": [
    "![Figura 6](img/Aharanov-Bohm/img6.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "60214a04",
   "metadata": {},
   "source": [
    "Vamos criar um laço do tipo `for` varrendo todos os valores de fluxo magnético do array `phi`. Modificamos o Hamiltoniano dos sítios atômicos sob o ramo de corte ilustrado na figura abaixo. Para cada valor de fluxo magnético repetiu-se as tarefas: finalizar o Hamiltoniano do sistema, calcular a matriz de espalhamento e calcular a probabilidade de transmissão:"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "91120a83",
   "metadata": {},
   "source": [
    "![Figura 7](img/Aharanov-Bohm/img7.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "d429db3d",
   "metadata": {},
   "outputs": [],
   "source": [
    "for i in range(200):\n",
    "    for j in range(1,10):\n",
    "        H[lattice(1, j - r_ext), lattice(0, j - r_ext)] \\\n",
    "            = -t*np.exp(2j*np.pi*phi[i])\n",
    "    Hf = H.finalized()\n",
    "    scatter_matrix = kwant.smatrix(Hf, 0.15*t)\n",
    "    conductance[i] =\\\n",
    "        scatter_matrix.transmission(1, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e3acd1ab",
   "metadata": {},
   "source": [
    "Vamos obter o gráfico da condutância em unidades de $e^{2}/h$ em função do fluxo magnético em unidades de $\\left(h/e\\right)$ da seguinte forma:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "399eb719",
   "metadata": {
    "scrolled": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 800x500 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize = (8,5))\n",
    "\n",
    "plt.plot(phi, conductance, color = 'deeppink', label = 'Simulação')\n",
    "plt.plot(ratio_phi, T, color = 'indigo', label = 'Teórico')\n",
    "plt.title('Efeito de Aharonov-Bohm')\n",
    "plt.xlabel(r'$\\phi = BS/(h/e)$')\n",
    "plt.ylabel(r'$g$ em unidades de $(e^2/h)$')\n",
    "\n",
    "plt.legend(loc = 'best')\n",
    "opt_plot()\n",
    "plt.savefig('Efeito de Aharonov-Bohm.png', dpi = 400)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2d07b89c",
   "metadata": {},
   "source": [
    "$\\blacksquare$"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "2a0c21ea",
   "metadata": {},
   "source": [
    "Comparando a curva obtida acima com o gráfico das oscilações de Aharonov-Bohm em um anel quântico obtidas no seção anterior, nota-se que são muito semelhantes, o que demonstra que para os parâmetros utilizados, essas oscilações são mais relevantes\n",
    "que os demais efeitos possíveis."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "46a2158e",
   "metadata": {},
   "source": [
    "---"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "397a702a",
   "metadata": {},
   "source": [
    "## Referências"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f05c1ba2",
   "metadata": {},
   "source": [
    "**[1]** J.J. SAKURAI, *Modern Quantum Mechanics* (Addison-Wesley Publis Comp, New York, 1994). Disponível em: https://books.google.com.br/books/about/Modern_Quantum_Mechanics.html?id=N4I-AQAACAAJ&redir_esc=y"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d58eb4e9",
   "metadata": {},
   "source": [
    "**[2]** AHARONOV, Y.; BOHM, D. *Significance of electromagnetic potentials in the quantum theory*. Phys. Rev., American Physical Society, v. **115**, p. 485–491, Aug 1959. Disponível em: <https://link.aps.org/doi/10.1103/PhysRev.115.485>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f854cef1",
   "metadata": {},
   "source": [
    "**[3]** CHAMBERS, R. G. *Shift of an electron interference pattern by enclosed magnetic flux*. Phys. Rev. Lett., American Physical Society, v. **5**, p. 3–5, Jul 1960. Disponível em:<https://link.aps.org/doi/10.1103/PhysRevLett.5.3>. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "d0ab5673",
   "metadata": {},
   "source": [
    "**[4]** BROMLEY, D.; GREINER, W. *Quantum Mechanics: Special Chapters*. Springer Berlin Heidelberg, 2012. ISBN 9783642588471. Disponível em: <https://books.google.com.br/books?id=Ei7vCAAAQBAJ>. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a04128cb",
   "metadata": {},
   "source": [
    "**[5]** IHN, T. *Semiconductor Nanostructures: Quantum States and Electronic Transport*. OUP Oxford, 2010. ISBN 9780199534425. Disponível em: <https://books.google.com.br/books?id=UdgVDAAAQBAJ>. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "793c0767",
   "metadata": {},
   "source": [
    "**[6]** NAZAROV, Y.; BLANTER, Y. *Quantum Transport: Introduction to Nanoscience*. Cambridge University Press, 2009. ISBN 9781139478175. Disponível em: <https://books.google.com.br/books?id=bjmXJOFmqZIC>. "
   ]
  },
  {
   "cell_type": "markdown",
   "id": "242ce38f",
   "metadata": {},
   "source": [
    "**[7]** SANTOS, L. H.; WANG, J. *Symmetry-protected many-body aharonov-bohm effect*. Phys. Rev. B, American Physical Society, v. **89**, p. 195122, May 2014. Disponível em: <https://link.aps.org/doi/10.1103/PhysRevB.89.195122>."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f3c1ce58",
   "metadata": {},
   "source": [
    "---"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
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    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.8"
  }
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