{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Nanostructures out of equilibrium with KWANT\n", "\n", "### © Marko Petrović, University of Delaware\n", "[PHYS824: Nanophysics & Nanotechnology](https://wiki.physics.udel.edu/phys824) " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## What is covered in this notebook\n", "- Two terminal Landauer-Buttiker formula\n", " - Square lattice (spinless) with temperature smearing.\n", " - Square lattice with Rashba interaction.\n", " - Square lattice with disorder and transmission matrix eigenvalues.\n", " - Ring with AB oscillations.\n", "- Adding custom hopping in KWANT\n", "- Buttiker dephasing.\n", "- Spin Hall effect in four terminal device.\n", "- Topological Hall effect in four terminal device. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.1 Conductance in a two-terminal square ribbon" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we need to create a two-terminal ribbon on a square lattice." ] }, { "cell_type": "code", "execution_count": 594, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import kwant\n", "import matplotlib.pyplot\n", "\n", "\n", "def lead_along_x(pos):\n", " x, y = pos\n", " width = 3.5\n", " return abs(y) < 0.5*width \n", "\n", "def system_shape(pos):\n", " x, y = pos\n", " width = 3.5\n", " length = 20.0\n", " return abs(x) < 0.5*length and abs(y) < 0.5*width\n", "\n", "# Build the system\n", "sys = kwant.Builder()\n", "lat = kwant.lattice.square(norbs=1)\n", "\n", "v1, v2 = lat.prim_vecs\n", "t = 1. # Hopping energy\n", "\n", "left_direction = kwant.TranslationalSymmetry(-v1)\n", "lead_left = kwant.Builder(left_direction)\n", "\n", "# Create main scattering region\n", "sys[lat.shape(system_shape, (0, 0))] = 0.0\n", "sys[lat.neighbors()] = -t\n", "\n", "# Create left lead\n", "lead_left[lat.shape(lead_along_x, (0, 0))] = 0.0 \n", "lead_left[lat.neighbors()] = -t\n", "\n", "sys.attach_lead(lead_left)\n", "sys.attach_lead(lead_left.reversed())\n", "\n", "sys_f = sys.finalized() # Create finalized sytem\n", "kwant.plot(sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1.1 Transmission and scattering matrix\n", "\n", "To calculate transmission in a two-terminal device, use kwant.smatrix object to obtain the scattering matrix at a given energy. The obtained scattering matrix object has a method called transmission which is used to calculate transmission between any pair of the attached leads." ] }, { "cell_type": "code", "execution_count": 603, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "import numpy as np\n", "from matplotlib import pyplot as plt\n", "\n", "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 200)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys_f, energy)\n", "\n", " # Here, we calculate the transmission \n", " # from the first lead (left lead) \n", " # to the second lead (right lead). \n", " # Indexing starts at zero, and it\n", " # depends on the order in which \n", " # the leads were attached. Lead\n", " # which is attached first will get \n", " # the index zero, the one that is\n", " # attached second will get the index\n", " # one etc.\n", " \n", " # The transmission function is T(E) = Tr[t*t^\\dagger]\n", " # Transmission from the lead 0 to lead 1\n", " t10.append(smatrix.transmission(1, 0))\n", "\n", "t10 = np.array(t10)\n", "plt.figure(dpi=100)\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Fermi Energy (eV)', fontsize=12);\n", "plt.title('Zero-temperature conductance in a two-terminal device', fontsize=12)\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.1.2 Temperature smearing of the conductance\n", "\n", "Temperature smearing is performed by convolution \n", "$$ G(T, E_F) = \\frac{2e^2}{h}\\int_{-\\infty}^{+\\infty} T(E)\n", "\\left(-\\frac{\\partial f(E)}{\\partial E}\\right) dE $$ \n", "with a derivative of the Fermi-Dirac function\n", " $$ -\\frac{\\partial f(E)}{\\partial E} = \n", " \\frac{1}{4k_BT}{\\rm sech}^2\\left(\\frac{E-E_{\\rm F}}{2k_BT}\\right)$$" ] }, { "cell_type": "code", "execution_count": 604, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "SUM = 0.9998857350102481\n", "8Kb*T = 0.206808\n" ] }, { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "KB = 8.617e-5 # eV / K\n", "\n", "def F(energy, ef=0, temp=300.):\n", " n = 1.0 / (4 * KB * temp)\n", " return n * (1.0 / np.cosh((energy - ef) / (2*KB*temp)))**2\n", "\n", "ens = np.linspace(-0.25, 0.25, 100)\n", "plt.figure(dpi=100)\n", "de = ens[1] - ens[0]\n", "plt.plot(ens, F(ens)*de);\n", "print('SUM = ', (F(ens)*de).sum())\n", "print(\"8Kb*T =\", 8*KB*300)\n", "plt.xlabel('Energy (eV)', fontsize=12);\n", "plt.ylabel(r'$-\\frac{\\partial f(E)}{\\partial E}$', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, we convolute the previously computed conductance with temperature." ] }, { "cell_type": "code", "execution_count": 605, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Compute transmission close to\n", "# one of the steps\n", "t10 = [] \n", "energies = np.linspace(-4, 4, 300)\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys_f, energy)\n", " t10.append(smatrix.transmission(1, 0))\n", "t10 = np.array(t10)\n", "\n", "\n", "t_conv = []\n", "temperature = 300.\n", "de = energies[1] - energies[0]\n", "for ef in energies:\n", " df = F(energies, ef=ef, temp=temperature)\n", " t_conv.append((df*t10*de).sum())\n", "\n", "t_conv = np.array(t_conv)\n", "plt.figure(dpi=150, figsize=(3, 3)) # Set figure size in inches\n", "plt.plot(energies, t10, color='gray', lw=1.0, label=r'T = 0 K');\n", "plt.plot(energies, t_conv, color='C3', lw=1.0, label=r'T = 300 K');\n", "plt.legend();\n", "plt.xlim(-4, 4);\n", "plt.xlabel('Fermi Energy (eV)')\n", "plt.ylabel(r'G $(\\frac{2e^2}{h}$)');" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.2 Rashba spin-orbit coupling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Rashba Hamiltonian on the square tight-binding lattice of sites ${\\bf m} = (m_x, m_y)$ is given by\n", "\n", "\n", "$$\n", "\\hat{H}=\\sum_{{\\bf m}\\sigma} \\varepsilon_{\\bf m} \n", "|{\\bf m}\\sigma\\rangle\\langle{\\bf m}\\sigma|+\n", "\\sum_{{\\bf mm'}\n", "\\sigma\\sigma'} \n", "t_{\\bf mm'}^{\\sigma\\sigma'}\n", "|{{\\bf m}\\sigma}\\rangle \n", "\\langle{{\\bf m'}\\sigma'}|.\n", "$$\n", " \n", " Its hopping parameters are non-trivial $2 \\times 2$ Hermitian matrices ${\\bf t}_{\\bf m'm}=({\\bf t}_{\\bf mm'})^\\dagger$ in the spin space\n", "\n", "$$\n", "{\\bf t}_{\\bf mm'}=\\left\\{\n", "\\begin{array}{cc}\n", "-t{\\bf I}_{\\rm 2}-it_{\\rm SO}\\hat{\\sigma}_y &\n", "({\\bf m}={\\bf m}'+{\\bf e}_x)\\\\\n", "-t{\\bf I}_{\\rm 2}+it_{\\rm SO}\\hat{\\sigma}_x & ({\\bf m}={\\bf m}'+{\\bf e}_y)\n", "\\end{array}\\right.,\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we need to define unit matrix $I_2$ and Pauli matrices\n", "\n", "$I_2 = \\left(\\begin{matrix} 1 & 0 \\\\ 0 & 1\\end{matrix}\\right) $,\n", "$\\sigma_x = \\left(\\begin{matrix} 0 & 1 \\\\ 1 & 0\\end{matrix}\\right) $,\n", "$\\sigma_y = \\left(\\begin{matrix} 0 & -i \\\\ i & 0\\end{matrix}\\right) $,\n", "$\\sigma_z = \\left(\\begin{matrix} 1 & 0 \\\\ 0 & -1\\end{matrix}\\right) $" ] }, { "cell_type": "code", "execution_count": 606, "metadata": {}, "outputs": [], "source": [ "unit = np.array([[1, 0], [0, 1]])\n", "sigma_x = np.array([[0, 1], [1, 0]])\n", "sigma_y = np.array([[0, -1j], [1j, 0]])\n", "sigma_z = np.array([[1, 0], [0, -1]])" ] }, { "cell_type": "code", "execution_count": 578, "metadata": {}, "outputs": [], "source": [ "def make_rashba_system(rsoc=1.0, t=1.0, width=3., length=4.):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return (y > 0) and (y <= width) \n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " in_x = (x > 0) and (x <= length)\n", " in_y = (y > 0) and (y <= width)\n", " return in_x and in_y\n", " \n", " def rashba(site1, site2):\n", " x1, y1 = site1.pos\n", " x2, y2 = site2.pos\n", " \n", " # Check if two sites are connected\n", " # with hopping along x-direction\n", " # (Then they have the same y-coordinate)\n", " hopping_along_x = abs(y2 - y1) < 1.e-6 \n", " if hopping_along_x: \n", " hopping = -t*unit - 1j*rsoc*sigma_y\n", " else: # Set hopping along y\n", " hopping = -t*unit + 1j*rsoc*sigma_x\n", " \n", " # Notice that here hoppings are not scalars\n", " # but [2 x 2] matrices\n", " return hopping\n", "\n", " # Build the system\n", " sys = kwant.Builder()\n", " # Notice that there are now two orbitals per site\n", " lat = kwant.lattice.square(norbs=2)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " # Create main scattering region\n", " sys[lat.shape(system_shape, (1, 1))] = 0*unit\n", " sys[lat.neighbors()] = rashba\n", "\n", " # Create left lead\n", " lead_left[lat.shape(lead_along_x, (1, 1))] = 0*unit \n", " lead_left[lat.neighbors()] = rashba\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", "\n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "code", "execution_count": 607, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sys, lead = make_rashba_system(width=2, length=3, rsoc=1.0)\n", "kwant.plot(sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, compute dispersion and transmission in this ribbon" ] }, { "cell_type": "code", "execution_count": 610, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" }, { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 200)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys, energy)\n", " t10.append(smatrix.transmission(1, 0))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "kwant.plotter.bands(lead);\n", "t10 = np.array(t10)\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Fermi Energy (eV)', fontsize=12);\n", "plt.title('Zero-temperature conductance in a two-terminal Rashba device',\n", " fontsize=12);\n", "plt.ylabel(r'G ($\\frac{e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.3 Introducing Anderson disorder" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Anderson Hamiltonian on the square tight-binding lattice \n", "of sites ${\\bf m} = (m_x, m_y)$ is given by\n", "\n", "$$\n", "\\hat{H}=\\sum_{{\\bf m}} \\varepsilon_{\\bf m} \n", "|{\\bf m}\\rangle\\langle{\\bf m}|+\n", "\\sum_{{\\bf mm'}} \n", "t_{\\bf mm'}\n", "|{{\\bf m}}\\rangle \n", "\\langle{{\\bf m'}}|.\n", "$$\n", "\n", "The on-site potential is a uniform random variable\n", "$\\varepsilon_{\\bf m} \\in [-W/2,W/2]$ modeling short range isotropic scattering." ] }, { "cell_type": "code", "execution_count": 548, "metadata": {}, "outputs": [], "source": [ "def make_system(w=5, t=-1.0, width=3, length=4):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return (y > 0) and (y <= width) \n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " in_x = (x > 0) and (x <= length)\n", " in_y = (y > 0) and (y <= width)\n", " return in_x and in_y\n", " \n", " def random_potential(site):\n", " pot = np.random.random()\n", " pot_w = w*(2*pot - 1)/2. \n", " return pot_w\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " # Create main scattering region\n", " sys[lat.shape(system_shape, (1, 1))] = random_potential\n", " sys[lat.neighbors()] = -t\n", "\n", " # Create left lead (no potential disorder)\n", " lead_left[lat.shape(lead_along_x, (1, 1))] = 0.\n", " lead_left[lat.neighbors()] = -t\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", " \n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3.2 Plot onsite potential" ] }, { "cell_type": "code", "execution_count": 612, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sys, lead = make_system(w=0.5, length=20, width=10)\n", "np.random.seed(5)\n", "h = sys.hamiltonian_submatrix()\n", "v = np.diag(h)\n", "kwant.plotter.map(sys, v.real);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3.3 Compute conductance using transmission matrix" ] }, { "cell_type": "code", "execution_count": 613, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 100)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(sys, energy)\n", " # Note, you need to set the seed\n", " # each time you call a solver\n", " np.random.seed(2) \n", " tmat = smatrix.submatrix(1, 0)\n", " tt = np.dot(tmat, tmat.conj())\n", " t10.append(np.trace(tt))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "t10 = np.array(t10)\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Fermi Energy (eV)', fontsize=12);\n", "plt.title('Zero-temperature conductance in a two-terminal device', fontsize=12)\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.3.4 Eigenvalues of the transmission matrix" ] }, { "cell_type": "code", "execution_count": 614, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "seeds = np.arange(100) # Do the averaging over 10 distributions\n", "t_evals = []\n", "\n", "for seed in seeds:\n", " smatrix = kwant.smatrix(sys, 0.)\n", " np.random.seed(seed) \n", " tmat = smatrix.submatrix(1, 0)\n", " tt = np.dot(tmat, tmat.conj())\n", " evals = np.linalg.eigvals(tt)\n", " t_evals = t_evals + list(evals)\n", "\n", "bins = np.linspace(0, 1, 100)\n", "plt.figure(dpi=100, figsize=(3, 3));\n", "plt.hist(t_evals, bins=bins);\n", "plt.xlabel('Transmission Eigenvalue', fontsize=12);\n", "plt.ylabel('P(T)', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.4 Introducing vacancy disorder" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In a similar way in which we add sites to the system, we use the delete (del) command to remove sites from the system. Notice that\n", "sites can only be removed from a system which is not finalized." ] }, { "cell_type": "code", "execution_count": 615, "metadata": {}, "outputs": [], "source": [ "def make_disordered_system(seed=0, nvac=5, t=-1.0, width=3, length=4):\n", " \"\"\"\n", " Parameters\n", " ----------\n", " seed : integer\n", " Determines how vacancies are sampled. Each\n", " integer will produce a unique distribution\n", " of vacancies\n", " nvac : integer\n", " Number of vacancies in the system\n", " \"\"\"\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return (y > 0) and (y <= width) \n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " in_x = (x > 0) and (x <= length)\n", " in_y = (y > 0) and (y <= width)\n", " return in_x and in_y\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " # Create main scattering region\n", " sys[lat.shape(system_shape, (1, 1))] = 0\n", " sys[lat.neighbors()] = -t\n", "\n", " # Create left lead\n", " lead_left[lat.shape(lead_along_x, (1, 1))] = 0\n", " lead_left[lat.neighbors()] = -t\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", " \n", " np.random.seed(seed)\n", " \n", " nv = 0\n", " lengths = np.arange(1, length+1)\n", " widths = np.arange(1, width+1)\n", " nv = 0 \n", " while nv < nvac:\n", " i = np.random.randint(length)+1\n", " j = np.random.randint(width)+1\n", " try:\n", " del sys[lat(i, j)]\n", " nv += 1\n", " except KeyError:\n", " continue\n", " \n", "\n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "code", "execution_count": 616, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "sys, lead = make_disordered_system(seed=2, length=10, width=10, nvac=3)\n", "kwant.plot(sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 1.5 Aharonov-Bohm oscillations" ] }, { "cell_type": "code", "execution_count": 620, "metadata": {}, "outputs": [], "source": [ "def make_ring(t=1.0, out_radius=10, in_radius=5, width=4, length=5.):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return abs(y) < 0.5*width\n", "\n", " def system_shape(pos):\n", " x, y = pos\n", " r = np.sqrt(x**2 + y**2)\n", " in_outer = r < out_radius \n", " in_inner = r < in_radius\n", " in_ring = in_outer and not in_inner\n", " return in_ring\n", " \n", " def bfield(site1, site2, flux):\n", " x1, y1 = site1.pos\n", " x2, y2 = site2.pos\n", " if x1 == -1 and y1 < 0 and y1 == y2: \n", " hop = -t*np.exp(-1j*flux)\n", " else:\n", " hop = -t\n", " return hop\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " lead_left = kwant.Builder(left_direction)\n", "\n", " r_cent = 0.5*(in_radius + out_radius)\n", " sys[lat.shape(system_shape, (r_cent, 0))] = 0.0\n", " sys[lat.neighbors()] = bfield \n", "\n", " lead_left[lat.shape(lead_along_x, (0, 0))] = 0.\n", " lead_left[lat.neighbors()] = -t\n", "\n", " sys.attach_lead(lead_left)\n", " sys.attach_lead(lead_left.reversed())\n", " \n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = lead_left.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "code", "execution_count": 618, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "ring_sys, lead = make_ring(in_radius=5, out_radius=13, width=10, length=20)\n", "kwant.plot(ring_sys);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.5.1 Transmission at zero magnetic field" ] }, { "cell_type": "code", "execution_count": 621, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "energies = np.linspace(-5, 5, 100)\n", "\n", "for energy in energies:\n", " smatrix = kwant.smatrix(ring_sys, energy, params={'flux':0.})\n", " t10.append(smatrix.transmission(1, 0))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "plt.plot(energies, t10, color='C0');\n", "plt.xlabel('Energy (eV)', fontsize=12);\n", "plt.title('Conductance in a two-terminal device', fontsize=12)\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);\n", "plt.xlim(-5, 5);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1.5.2 Aharonov-Bohm oscillations" ] }, { "cell_type": "code", "execution_count": 460, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "t10 = [] # Transmission from lead 0 to lead 1\n", "fluxes = np.linspace(0.1, 30., 100)\n", "\n", "for flux in fluxes:\n", " smatrix = kwant.smatrix(ring_sys, 3.85, params={'flux': flux})\n", " t10.append(smatrix.transmission(1, 0))\n", " \n", "plt.figure(dpi=100, figsize=(3, 3));\n", "plt.plot(fluxes/(2*np.pi), t10, color='C0');\n", "plt.xlabel('Magnetic flux', fontsize=12);\n", "plt.ylabel(r'G ($\\frac{2e^2}{h}$)', fontsize=12);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 2. Büttiker dephasing" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Introducing an additional third lead in a two-terminal device will\n", "lead to Büttiker dephasing, where the dephased transmission $\\tilde{T}_{21}$\n", "between leads 1 and 2 is given by\n", "\n", "$$ \\tilde{T}_{21}(E) = T_{\\rm coherent}(E) + T_{\\rm incoherent}(E) =\n", "T_{21}(E) + \\frac{T_{23}(E)T_{31}(E)}{T_{31}(E) + T_{23}(E)}\n", "$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "First, we will modify our make_ring function, so that the system now\n", "has three leads. Also, we will add an option to switch from ring into a rectangle" ] }, { "cell_type": "code", "execution_count": 103, "metadata": {}, "outputs": [], "source": [ "def make_buttiker_system(t=1.0, out_radius=10, in_radius=5, width=4, length=20.,\n", " lead_pos=0, make_ring=True, attach_probe=True,\n", " pot=0):\n", " \n", " def lead_along_x(pos):\n", " x, y = pos\n", " return abs(y) <= 0.5*width\n", " \n", " def lead_along_y(pos):\n", " x, y = pos\n", " return abs(x-lead_pos) <= 0.5*width\n", "\n", " def ring_shape(pos):\n", " x, y = pos\n", " r = np.sqrt(x**2 + y**2)\n", " in_outer = r < out_radius \n", " in_inner = r < in_radius\n", " in_ring = in_outer and not in_inner\n", " return in_ring\n", " \n", " def pot_function(site):\n", " \"\"\"Add potential close to the left lead\"\"\"\n", " x, y = site.pos\n", " if make_ring:\n", " if (x < -out_radius + 3):\n", " V = pot\n", " else:\n", " V = 0\n", " else:\n", " if (x < -0.5*length + 3):\n", " V = pot\n", " else:\n", " V = 0\n", " return V\n", " \n", " def rectangle(pos):\n", " x, y = pos\n", " in_x = abs(x) <= 0.5*length\n", " in_y = abs(y) <= 0.5*width\n", " return in_x and in_y\n", " \n", " sys = kwant.Builder()\n", " lat = kwant.lattice.square(norbs=1)\n", "\n", " v1, v2 = lat.prim_vecs\n", "\n", " left_direction = kwant.TranslationalSymmetry(-v1)\n", " left_lead = kwant.Builder(left_direction)\n", " \n", " down_direction = kwant.TranslationalSymmetry(-v2)\n", " down_lead = kwant.Builder(down_direction)\n", "\n", " r_cent = 0.5*(in_radius + out_radius)\n", " \n", " if make_ring:\n", " sys[lat.shape(ring_shape, (r_cent, 0))] = pot_function\n", " else:\n", " if abs(lead_pos) > 0.5*(length-width):\n", " raise ValueError('Bad lead_pos parameter. Please set it within'\n", " 'the (-length/2+width/2, lenght/2-width/2) range')\n", " sys[lat.shape(rectangle, (0, 0))] = pot_function\n", " \n", " sys[lat.neighbors()] = -t \n", "\n", " left_lead[lat.shape(lead_along_x, (0, 0))] = 0.\n", " left_lead[lat.neighbors()] = -t\n", " \n", " down_lead[lat.shape(lead_along_y, (lead_pos, 0))] = 0.\n", " down_lead[lat.neighbors()] = -t\n", " \n", " # Pay attention to the order in which the leads are\n", " # attached.\n", " sys.attach_lead(left_lead)\n", " sys.attach_lead(left_lead.reversed())\n", " if attach_probe:\n", " sys.attach_lead(down_lead) \n", " \n", " \n", " sys_f = sys.finalized() # Create finalized sytem\n", " lead_f = left_lead.finalized() # Create finalized lead\n", " return sys_f, lead_f" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.1 Dephasing transmission as a function of energy" ] }, { "cell_type": "code", "execution_count": 108, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Make the system with three leads\n", "sys_3lead, lead = make_buttiker_system(out_radius=10, in_radius=5, length=20.,\n", " width=2, lead_pos=0, make_ring=False)\n", "\n", "# Make identical system, but only with two leads\n", "sys_2lead, lead = make_buttiker_system(out_radius=10, in_radius=5, length=20.,\n", " width=2, lead_pos=0, make_ring=False,\n", " attach_probe=False)\n", "kwant.plot(sys_3lead);\n", "\n", "energies = np.linspace(-3, 3, 100)\n", "t_3lead = []\n", "t_2lead = []\n", "\n", "for e in energies:\n", " smatrix_3lead = kwant.smatrix(sys_3lead, e)\n", " smatrix_2lead = kwant.smatrix(sys_2lead, e)\n", " t21 = smatrix_3lead.transmission(1, 0)\n", " t31 = smatrix_3lead.transmission(2, 0)\n", " t23 = smatrix_3lead.transmission(1, 2)\n", " t_3lead.append(t21 + (t23*t31)/(t23+t31))\n", " \n", " t_2lead.append(smatrix_2lead.transmission(1, 0))\n", "\n", "plt.figure(dpi=140, figsize=(3, 3))\n", "plt.plot(energies, t_2lead, color='gray', label='no dephasing')\n", "plt.plot(energies, t_3lead, color='red', label='dephased')\n", "plt.legend()\n", "plt.xlabel('Fermi energy (t)');\n", "plt.ylabel('$\\\\tilde{T}_{21}$ ');\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2.2 Dephasing transmission as a function of lead position" ] }, { "cell_type": "code", "execution_count": 109, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "\n", "positions = np.arange(-30, 30)\n", "t_3lead = []\n", "\n", "for pos in positions:\n", " sys_3lead, lead = make_buttiker_system(length=62., pot=0.5,\n", " width=2, lead_pos=pos, make_ring=False)\n", " smatrix_3lead = kwant.smatrix(sys_3lead, 0.)\n", " t21 = smatrix_3lead.transmission(1, 0)\n", " t31 = smatrix_3lead.transmission(2, 0)\n", " t23 = smatrix_3lead.transmission(1, 2)\n", " t_3lead.append(t21 + (t23*t31)/(t23+t31))\n", "\n", "plt.figure(dpi=140, figsize=(3, 3))\n", "plt.plot(positions, t_3lead, color='red', label='dephased')\n", "plt.legend()\n", "plt.xlabel('Lead position');\n", "plt.ylabel('$\\\\tilde{T}_{21}$ ');\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 3. Spin Hall effect in a four-terminal device" ] }, { "cell_type": "code", "execution_count": 126, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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\n", 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" }, { "name": "stdout", "output_type": "stream", "text": [ " Energy = 0.100000" ] }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from math import sqrt\n", "import random\n", "import itertools as it\n", "import tinyarray as ta\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import kwant\n", "from sympy import S, Eq, solve, Symbol\n", "\n", "\n", "class Honeycomb(kwant.lattice.Polyatomic):\n", " \"\"\"Honeycomb lattice with methods for dealing with hexagons\"\"\"\n", "\n", " def __init__(self, name=''):\n", " prim_vecs = [[0.5, sqrt(3)/2], [1, 0]] # Bravais lattice vectors\n", " # offset the lattice so that it is symmetric around x and y axes\n", " basis_vecs = [[-0.5, -1/sqrt(12)], [-0.5, 1/sqrt(12)]]\n", " super(Honeycomb, self).__init__(prim_vecs, basis_vecs, name)\n", " self.a, self.b = self.sublattices\n", "\n", " def hexagon(self, tag):\n", " \"\"\" Get sites belonging to hexagon with the given tag.\n", " Returns sites in counter-clockwise order starting\n", " from the lower-left site.\n", " \"\"\"\n", " tag = ta.array(tag)\n", " # a-sites b-sites\n", " deltas = [(0, 0), (0, 0),\n", " (1, 0), (0, 1),\n", " (0, 1), (-1, 1)]\n", " lats = it.cycle(self.sublattices)\n", " return (lat(*(tag + delta)) for lat, delta in zip(lats, deltas))\n", "\n", " def hexagon_neighbors(self, tag, n=1):\n", " \"\"\" Get n'th nearest neighbor hoppings within the hexagon with\n", " the given tag.\n", " \"\"\"\n", " hex_sites = list(self.hexagon(tag))\n", " return ((hex_sites[(i+n)%6], hex_sites[i%6]) for i in range(6))\n", "\n", "def random_placement(builder, lattice, density):\n", " \"\"\" Randomly selects hexagon tags where adatoms can be placed.\n", " This avoids the edge case where adatoms would otherwise\n", " be placed on incomplete hexagons at the system boundaries.\n", " \"\"\"\n", " assert 0 <= density <= 1\n", " system_sites = builder.sites()\n", "\n", " def hexagon_in_system(tag):\n", " return all(site in system_sites for site in lattice.hexagon(tag))\n", "\n", " # get set of tags for sites in system (i.e. tags from only one sublattice)\n", " system_tags = (s.tag for s in system_sites if s.family == lattice.a)\n", " # only allow tags which have complete hexagons in the system\n", " valid_tags = list(filter(hexagon_in_system, system_tags))\n", " N = int(density * len(valid_tags))\n", " total_hexagons=len(valid_tags)\n", " valuef=random.sample(valid_tags, N)\n", " return valuef\n", "\n", "def cross(W, L):\n", " def shape(pos):\n", " return ((-W <= pos[0] <= W and -L <= pos[1] <= L) or # vertical\n", " (-W <= pos[1] <= W and -L <= pos[0] <= L)) # horizontal\n", " return shape\n", "\n", "## Pauli matrices ##\n", "sigma_0 = ta.array([[1, 0], [0, 1]]) # identity\n", "sigma_x = ta.array([[0, 1], [1, 0]])\n", "sigma_y = ta.array([[0, -1j], [1j, 0]])\n", "sigma_z = ta.array([[1, 0], [0, -1]])\n", "\n", "## Hamiltonian value functions ##\n", "\n", "def onsite_potential(site, params):\n", " return params['ep'] * sigma_0\n", "\n", "def potential_shift(site, params):\n", " return params['mu'] * sigma_0\n", "\n", "def kinetic(site_i, site_j, params):\n", " return -params['gamma'] * sigma_0\n", "\n", "def rashba(site_i, site_j, params):\n", " d_ij = site_j.pos - site_i.pos\n", " rashba = 1j * params['V_R'] * (sigma_x * d_ij[1] - sigma_y * d_ij[0])\n", " return rashba + kinetic(site_i, site_j, params)\n", "\n", "def spin_orbit(site_i, site_j, params):\n", " so = (1j/3.) * params['V_I'] * sigma_z\n", " return so\n", "\n", "lat = Honeycomb()\n", "pv1, pv2 = lat.prim_vecs\n", "ysym = kwant.TranslationalSymmetry(pv2 - 2*pv1) # -y direction\n", "xsym = kwant.TranslationalSymmetry(-pv2) # -x direction\n", "\n", "# Adatom lattice, for visualization only\n", "adatom_lat = kwant.lattice.Monatomic(lat.prim_vecs, name='adatom')\n", "\n", "def site_size(s): \n", " return 0.25 if s.family in lat.sublattices else 0.35\n", "\n", "def site_color(s): \n", " return '#000000' if s.family in lat.sublattices else '#de962b'\n", "\n", "def create_lead_h(W, symmetry, axis=(0, 0)):\n", " lead = kwant.Builder(symmetry)\n", " lead[lat.wire(axis, W)] = 0. * sigma_0\n", " lead[lat.neighbors(1)] = kinetic\n", " return lead\n", "\n", "def create_lead_v(L,W, symmetry):\n", " axis=(0, 0)\n", " lead = kwant.Builder(symmetry)\n", " lead[lat.wire(axis, W)] = 0. * sigma_0\n", " lead[lat.neighbors(1)] = kinetic\n", " return lead\n", "\n", "def create_hall_cross(W, L, adatom_density=0.2, show_adatoms=False):\n", " ## scattering region ##\n", " sys = kwant.Builder()\n", " sys[lat.shape(cross(W, L), (0, 0))] = onsite_potential\n", " sys[lat.neighbors(1)] = kinetic\n", "\n", " adatoms = random_placement(sys, lat, adatom_density)\n", "\n", " sys[(lat.hexagon(a) for a in adatoms)] = potential_shift\n", " sys[(lat.hexagon_neighbors(a, 1) for a in adatoms)] = rashba\n", " sys[(lat.hexagon_neighbors(a, 2) for a in adatoms)] = spin_orbit\n", " if show_adatoms:\n", " # no hoppings are added so these won't affect the dynamics; purely cosmetic\n", " sys[(adatom_lat(*a) for a in adatoms)] = 0\n", " ## leads ##\n", " leads = [create_lead_h(W, xsym)]\n", " leads += [create_lead_v(L,W, ysym)]\n", " leads += [lead.reversed() for lead in leads] # right and bottom leads\n", " for lead in leads:\n", " sys.attach_lead(lead)\n", " return sys\n", "\n", "def plot_ldos(sys, Es, params):\n", " fsys = sys.finalized()\n", " ldos = kwant.ldos(fsys, energy=Es, args=(params,))\n", " ldos = ldos[::2] + ldos[1::2] # sum spins\n", " kwant.plotter.map(fsys, ldos, vmax=0.1)\n", "\n", "def plot_conductance(sys, energies, lead_i, lead_j, params):\n", " fsys = sys.finalized()\n", " data = []\n", "\n", " for energy in energies:\n", " smatrix = kwant.greens_function(fsys, energy, args=(params,))\n", " data.append(smatrix.transmission(lead_i,lead_j))\n", "\n", " plt.figure()\n", " plt.plot(energies, data)\n", " plt.xlabel(\"energy (t)\")\n", " plt.ylabel(r'Conductance ($e^2/h$)')\n", " plt.show()\n", "\n", "def plot_spin_conductance(sys, energies,lead_i,lead_j, params):\n", " fsys = sys.finalized()\n", " data = []\n", "\n", " for energy in energies:\n", " smatrix = kwant.greens_function(fsys, energy, args=(params,))\n", " ttdagger = smatrix._a_ttdagger_a_inv(lead_i, lead_j)\n", " sigma_z_matrix = np.kron(np.eye(int(len(ttdagger)/2)),sigma_z) \n", " data.append(np.trace(sigma_z_matrix.dot(ttdagger)).real)\n", " plt.figure()\n", " plt.plot(energies, data)\n", " plt.xlabel(\"energy (t)\")\n", " plt.ylabel(r'Spin conductance ($e^2/h$)')\n", " plt.show()\n", "\n", "def solvematrix4(G,I0,I2,V1,V3):\n", " # I=GxV\n", " I1,I3,V0,V2=S('I1 I3 V0 V2'.split())\n", " equations = [Eq(I0, G[0][0]*V0+G[0][1]*V1+G[0][2]*V2+G[0][3]*V3), \\\n", " Eq(I1, G[1][0]*V0+G[1][1]*V1+G[1][2]*V2+G[1][3]*V3), \\\n", " Eq(I2, G[2][0]*V0+G[2][1]*V1+G[2][2]*V2+G[2][3]*V3), \\\n", " Eq(I3, G[3][0]*V0+G[3][1]*V1+G[3][2]*V2+G[3][3]*V3)]\n", " return solve(equations, [I1,I3,V0,V2], set=True, dict=False, rational=None, manual=True, minimal=True, particular=True, implicit=False, quick=True)\n", "\n", "def plot_SH_angle(sys, energies, params):\n", " fsys = sys.finalized()\n", " data = []\n", "\n", " I0 = 0.\n", " I2 = 0.\n", " V1 = 1.\n", " V3 = 0.\n", "\n", " for energy in energies:\n", " print(\"\\r Energy = %.5f\" % energy, end='')\n", " smatrix = kwant.greens_function(fsys, energy, args=(params,))\n", " G = np.zeros((4, 4))\n", " for i in range(4):\n", " a = 0\n", " for j in range(4):\n", " G[i,j] = smatrix.transmission(i, j)\n", " if i != j: a+=G[i,j]\n", " G[i,i]=-a\n", " a = solvematrix4(G, I0, I2, V1, V3)[1]\n", " result = list(a)\n", "\n", " I1 = result[0][0]\n", " I3 = result[0][1]\n", " V0 = result[0][2]\n", " V2 = result[0][3]\n", "\n", " Gspin = np.zeros((4, 4))\n", " for i in range(4):\n", " a = 0\n", " for j in range(4):\n", " ttdagger = smatrix._a_ttdagger_a_inv(i, j)\n", " sigma_z_matrix = np.kron(np.eye(int(len(ttdagger)/2)),sigma_z) \n", " Gspin[i,j] = np.trace(sigma_z_matrix.dot(ttdagger)).real\n", " if i != j: a+=Gspin[i,j]\n", " Gspin[i,i]=-a\n", "\n", " IS0 = Gspin[1,0] * (V1-V0) + Gspin[2,0]*(V2-V0) + Gspin[3,0] * (V3-V0)\n", " data.append(IS0/I1)\n", "\n", " plt.figure()\n", " plt.plot(energies, data)\n", " plt.xlabel(\"Energy (t)\")\n", " plt.ylabel(\"Spin Hall Angle\")\n", " plt.show()\n", "\n", "if __name__ == '__main__':\n", " params = dict(gamma=1., ep=0, mu=0.1, \n", " V_I=0.007, V_R=0.0165) # Au adatoms\n", "\n", " W = 16\n", " L = 32\n", " adatom_density=0.01\n", " # adatom_density=0.15\n", " # W = 8\n", " # L = 16\n", "\n", " sys = create_hall_cross(W, L, adatom_density, show_adatoms=True)\n", " kwant.plot(sys, site_color=site_color, site_size=site_size)\n", "\n", " sys = create_hall_cross(W, L, adatom_density, show_adatoms=False)\n", " plot_ldos(sys, 1e-5, params)\n", " \n", " Es = np.linspace(-0.1, 0.1, 101)\n", " plot_spin_conductance(sys, Es, 1, 0, params) # T01\n", " plot_conductance(sys, Es, 1, 0, params) # TS01\n", "\n", " plot_SH_angle(sys, Es, params)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# 4. Topological Hall effect in a four-terminal device due to skyrmion" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "A magnetic texture placed on top of the tight-binding system, for instance a skyrmion,\n", "would modify its Hamiltonian\n", "\n", "$$H = - t \\sum_{\\langle ij\\rangle} |i\\rangle\\langle j| +\n", " \\sum_{i} V_i \\ \\ |i\\rangle\\langle i|$$\n", "through its onsite energy\n", "$$V_i = J \\ m ( r) \\cdot \\sigma $$\n", "\n", "Here, the skyrmion is given by\n", "$$ m ( r) = \\left(x/r \\sin\\theta \\ , \\ y/r \\sin\\theta \\ ,\\ \\cos\\theta \\right) $$\n", "\n", "$$\\theta (r) = \\tanh \\frac{r-r_0}{\\delta}$$" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 4.1 Plotting the skyrmion" ] }, { "cell_type": "code", "execution_count": 122, "metadata": {}, "outputs": [], "source": [ "import matplotlib.pyplot as plt\n", "\n", "def plot_skyrmion(r0=15, delta=5, nx=20, ny=20, rmax=30):\n", " x_points = np.linspace(-rmax, rmax, nx)\n", " y_points = np.linspace(-rmax, rmax, ny)\n", " x, y = np.meshgrid(x_points, y_points)\n", " r = np.sqrt(x**2 + y**2)\n", " theta = np.tanh((r0 - r)/delta)\n", " mx = (x/r)*np.sin(theta)\n", " my = (y/r)*np.sin(theta)\n", " mz = np.cos(theta)\n", " \n", " plt.figure(dpi=150, figsize=(3, 3))\n", " plt.quiver(x, y, mx, my, mz, cmap='bwr')\n", " plt.title('Magnetic texture (skyrmion)')\n", " plt.xlabel('$x$')\n", " plt.ylabel('$y$')" ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plot_skyrmion()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 5.2 Computing the Hall resistance\n", "\n", "According to the Landauer-Büttiker formula, the conductance in a\n", "four-terminal device given in the matrix form is\n", "\n", "\n", "$$ \\left(\\begin{matrix} I_1 \\\\ I_2 \\\\ I_3 \\\\ I_4 \\end{matrix} \\right) =\n", " \\left(\n", " \\begin{matrix}\n", " G_{12} + G_{13} + G_{14} & -G_{12} & -G_{13} & -G{14} \\\\\n", " -G_{21} & G_{21} + G_{23} + G_{24} & -G_{23} & -G_{24} \\\\\n", " -G_{31} & -G_{32} & G_{31}+ G_{32} + G_{34} & -G_{34} \\\\\n", " -G_{41} & -G_{42} & -G_{43} & G_{41} + G_{42} + G_{43} \n", " \\end{matrix}\n", " \\right)\n", " \\left(\n", " \\begin{matrix}\n", " V_1 \\\\ V_2 \\\\ V_3 \\\\ V_4\n", " \\end{matrix}\n", " \\right),\n", "$$\n", "\n", "where the leads are indexed in the clockwise direction starting from the left lead.\n", "This system is not independent because current $I_4$ can be expressed using other three currents. Also, since currents only depend on voltage differences one voltage can be set as a reference point ($V_4 = 0$). The given system then reduces to three equations\n", "\n", "$$ \\left(\\begin{matrix} I_1 \\\\ I_2 \\\\ I_3 \\end{matrix} \\right) =\n", " \\left(\n", " \\begin{matrix}\n", " G_{12} + G_{13} + G_{14} & -G_{12} & -G_{13} \\\\\n", " -G_{21} & G_{21} + G_{23} + G_{24} & -G_{23} \\\\\n", " -G_{31} & -G_{32} & G_{31}+ G_{32} + G_{34} \\\\\n", " \\end{matrix}\n", " \\right)\n", " \\left(\n", " \\begin{matrix}\n", " V_1 \\\\ V_2 \\\\ V_3\n", " \\end{matrix}\n", " \\right),\n", "$$\n", "\n", "Inverting the conductance matrix, we get the resistance matrix\n", "\n", "$$ \\left(\\begin{matrix} V_1 \\\\ V_2 \\\\ V_3 \\end{matrix} \\right) =\n", " \\left(\n", " \\begin{matrix}\n", " R_{11} & R_{12} & R_{13} \\\\\n", " R_{21} & R_{22} & R_{23} \\\\\n", " R_{31} & R_{32} & R_{33} \\\\\n", " \\end{matrix}\n", " \\right)\n", " \\left(\n", " \\begin{matrix}\n", " I_1 \\\\ I_2 \\\\ I_3\n", " \\end{matrix}\n", " \\right),\n", "$$\n", "that is $\\mathbf{V} = \\mathbf{R}\\mathbf{I}$, where $\\mathbf{R} = \\mathbf{G}^{-1}$. " ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "code", "execution_count": 125, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "from types import SimpleNamespace\n", "from matplotlib import pyplot\n", "from math import cos, sin, pi\n", "import numpy as np\n", "import scipy.stats as reg\n", "import kwant\n", "from sympy import S, Eq, solve, Symbol\n", "\n", "lat = kwant.lattice.square()\n", "\n", "# Define unity and Pauli matrices\n", "s_0 = np.identity(2)\n", "s_z = np.array([[1, 0], [0, -1]])\n", "s_x = np.array([[0, 1], [1, 0]])\n", "s_y = np.array([[0, -1j], [1j, 0]])\n", "\n", "\n", "def HedgeHog(site, ps):\n", " \"\"\"Defines an onsite potential function in the \n", " main scattering region due to coupling with magnetic\n", " texture.\n", " \n", " Parameters\n", " ----------\n", " site : site object\n", " ps : input parameters\n", " \"\"\"\n", " \n", " x, y = site.pos\n", " r = (x**2 + y**2)**0.5\n", " theta = (np.pi/2)*(np.tanh((ps.r0 - r)/ps.delta) + 1)\n", " if r != 0:\n", " Ex = ((x/r)*np.sin(theta)*s_x +\n", " (y/r)*np.sin(theta)*s_y + \n", " np.cos(theta)*s_z)\n", " else:\n", " Ex = s_z\n", " return 4*s_0 + ps.Ex * Ex\n", " \n", "\n", "def Lead_Pot(site, ps):\n", " return 4*s_0 + ps.Ex * s_z\n", "\n", "def MakeSystem(ps, show=False):\n", " H = kwant.Builder()\n", "\n", " def shape_2DEG(pos):\n", " # Defines a four-terminal cross region\n", " x, y = pos\n", " in_x = (abs(x) < ps.L) and (abs(y) < ps.W)\n", " in_y = (abs(x) < ps.W) and (abs(y) < ps.L)\n", " return in_x or in_y\n", " \n", " H[lat.shape(shape_2DEG,(0, 0))] = HedgeHog\n", " H[lat.neighbors()] = -s_0\n", " \n", " # Define lead along the x-direction\n", " sym_x = kwant.TranslationalSymmetry((-1,0))\n", " H_lead_x = kwant.Builder(sym_x)\n", " shape_x = lambda pos: abs(pos[1])petrovic@udel.edu" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.8.3" } }, "nbformat": 4, "nbformat_minor": 4 }