{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# 001. Photoluminescence and absorption of triplet transitions in the nitrogen-vacancy center in diamond using Huang-Rhys theory" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In this notebook, we demonstrate how to use `PyPL` to compute vibrationally resolved photoluminescence (PL) and absorption spectra associated with the transition between the triplet excited state ($^3E$) and the triplet ground state ($^3A_2$) of the negatively charged nitrogen-vacancy center (NV$^-$) in diamond, using the Huang-Rhys (HR) theory and the generating function approach. [[1]](https://doi.org/10.1088/1367-2630/16/7/073026) [[2]](https://doi.org/10.1103/PhysRevMaterials.5.084603)\n", "\n", "The notebook is organized into four parts:\n", "\n", "1. Photoluminescence spectrum from atomic displacements\n", "\n", "2. Photoluminescence spectrum from forces\n", "\n", "3. Absorption spectrum from atomic displacements\n", "\n", "4. Temperature-dependent photoluminescence spectrum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 1. Photoluminescence spectrum from atomic displacements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "To compute the vibrationally resolved PL spectrum for the ${}^3\\!E \\to {}^3\\!A_2$ transition of the $\\text{NV}^-$ center in diamond, we require the equilibrium atomic coordinates of both the ${}^3\\!A_2$ and ${}^3\\!E$ states, as well as the phonon frequencies and eigenmodes evaluated at the equilibrium geometry of the ${}^3\\!A_2$ state.\n", "\n", "The equilibrium coordinates of the ${}^3\\!A_2$ ground state can be obtained from a density functional theory (DFT) calculation, for example, using the [Quantum ESPRESSO](https://www.quantum-espresso.org/) code. Input and pseudopotential files for this calculation are provided in the `001_nv_diamond_abs_pl/gs_dft` directory. The relevant output file is `001_nv_diamond_abs_pl/gs_dft/pwscf.xml`, which contains the optimized atomic positions.\n", "\n", "The equilibrium coordinates of the ${}^3\\!E$ excited state are obtained via a constrained-occupation DFT ($\\Delta$SCF) calculation. The corresponding input and output files are provided in `001_nv_diamond_abs_pl/es_dft`.\n", "\n", "Phonon frequencies and eigenmodes at the ${}^3\\!A_2$ equilibrium geometry are computed using the frozen-phonon approach with the [Phonopy](https://phonopy.github.io/phonopy/) package. The detailed procedure is described in `001_nv_diamond_abs_pl/phonon/README.md`, and the resulting data are stored in `001_nv_diamond_abs_pl/phonon/gs_ph_mesh.hdf5`.\n", "\n", "**Note**: The atoms in the ground-state DFT and excited-state $\\Delta$SCF calculations must appear in the same order to ensure correct mapping of displacements and phonon modes." ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "import numpy as np\n", "from scipy import constants\n", "import matplotlib.pyplot as plt\n", "\n", "plt.rcParams.update({'font.size': 12})\n", "\n", "blue = '#4285F4'\n", "red = '#DB4437'\n", "deep_violet = '#9D80B8'\n", "vibrant_purple = '#D391C2'\n", "soft_coral = '#F3B1BA'\n", "ocean_blue = '#81BFD6'\n", "goldenrod_yellow = '#EBD68F'\n", "emerald_green = '#02A650'\n", "\n", "from pypl.hr_solver import hr_solver\n", "from pypl.utils import *\n", "import os\n", "\n", "path = os.getcwd()\n", "os.chdir(path)" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "gs_phonon_file = '001_nv_diamond_abs_pl/phonon/gs_ph_mesh.hdf5'\n", "gs_file = '001_nv_diamond_abs_pl/gs_dft/pwscf.xml'\n", "es_file = '001_nv_diamond_abs_pl/es_cdft/pwscf.xml'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`PyPL` provides utility functions to extract and process data from these files." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "# Unit of freqs is THz\n", "gs_phonon_freqs, gs_phonon_modes = parse_phonopy_h5(gs_phonon_file)\n", "# Unit of coordinates and cell_parameters is Angstrom\n", "atomic_symbols, gs_coord, cell_parameters = parse_atoms_qexml(gs_file)\n", "atomic_symbols_2, es_coord, cell_parameters_2 = parse_atoms_qexml(es_file)\n", "\n", "# Ensure that both sets of atomic coordinates have consistent atomic symbols and cell parameters.\n", "assert atomic_symbols == atomic_symbols_2, 'Mismatch in atomic symbols between ground-state and excited-state structures.'\n", "assert np.max(np.abs(cell_parameters - cell_parameters_2)) < 1e-12, 'Mismatch in cell parameters between ground-state and excited-state structures.'" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Atomic masses must also be specified for all elements in the system; otherwise, `PyPL` will fall back to its default values." ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [], "source": [ "mass_list = {'C': 12.0107, 'N': 14.0067}" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We begin by computing the partial HR factor, which quantifies the coupling between the electronic transition and a specific phonon mode. This factor is then used to evaluate the vibrationally resolved PL spectrum via the generating function approach. The partial HR factor for phonon mode $k$ is given by:\n", "\\begin{equation}\n", "S_k = \\frac{\\omega_k \\Delta Q_k^2}{2\\hbar}\n", "\\end{equation}\n", "where $\\Delta Q_k$ is the mass-weighted displacement along mode $k$. It is evaluated as\n", "\\begin{equation}\n", "\\Delta Q_k = \\sum_{\\alpha=1}^N\\sum_{i=x,y,z}\\sqrt{M_{\\alpha}} \\Delta R_{\\alpha i} e_{k,\\alpha i}.\n", "\\end{equation}\n", "Here, $\\Delta R_{\\alpha i} = R_{\\alpha i}^{\\text{ES}} - R_{\\alpha i}^{\\text{GS}}$ is the Cartesian displacement of atom ${\\alpha}$ along direction $i$ between the excited-state (ES, ${{}^3\\!E}$) and ground-state (GS, ${}^3\\!A_2$) geometries, $M_\\alpha$ is the atomic mass, and $e_{k,\\alpha i}$ is the eigenvector component of phonon mode $k$." ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Huang-Rhys factors using atomic displacements.\n", "Total \\Delta Q is 6.529832366847e-01 amu^{0.5} \\AA\n", "Total Huang-Rhys factor is 2.985289200067e+00\n" ] } ], "source": [ "pl_use_dis = hr_solver()\n", "hrf_dict_pl_dis = pl_use_dis.compute_hrf_dis(gs_phonon_freqs, gs_phonon_modes, atomic_symbols, gs_coord, es_coord, cell_parameters, mass_list=mass_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "`hrf_dict_pl_dis` is a dictionary that contains the phonon frequencies (in rad/s) and the corresponding partial HR factors. We can inspect the phonon modes with the strongest electron–phonon coupling as follows:" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "index 64 freq: 62.3239 meV hrf: 8.3595e-01\n", "index 6 freq: 34.4922 meV hrf: 3.5594e-01\n", "index 36 freq: 49.0021 meV hrf: 3.2950e-01\n", "index 252 freq: 81.4371 meV hrf: 1.0780e-01\n", "index 30 freq: 48.2382 meV hrf: 8.3555e-02\n", "index 144 freq: 70.7789 meV hrf: 7.6982e-02\n", "index 5 freq: 34.3174 meV hrf: 6.6586e-02\n", "index 17 freq: 42.5984 meV hrf: 6.2820e-02\n", "index 122 freq: 68.2145 meV hrf: 5.7055e-02\n", "index 321 freq: 89.3907 meV hrf: 4.9803e-02\n" ] } ], "source": [ "indices = np.argsort(hrf_dict_pl_dis['hr_factors'])[-10:]\n", "for i in indices[::-1]:\n", " print('index %4d freq: % .4f meV hrf: % .4e' % (i + 1, hrf_dict_pl_dis['freqs'][i] * constants.hbar / constants.eV * 1e3, hrf_dict_pl_dis['hr_factors'][i]))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compute the spectral density of the HR factors defined as\n", "\\begin{equation}\n", "S(\\hbar\\omega) = \\sum_k S_k \\delta(\\hbar\\omega - \\hbar\\omega_k),\n", "\\end{equation}\n", "In practice, the Dirac $\\delta$-function is approximated by a Gaussian to account for the participation of a continuum of phonon modes. The Gaussian broadening is interpolated from the values specified in `sigma` (given in meV), which are empirically set to best match the experimental spectrum." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [], "source": [ "sigmas = [\n", " [3, 2], [3, 4], [3, 6],\n", " [6, 2], [6, 4], [6, 6],\n", "]\n", "\n", "spectral_density_pl_dis = []\n", "for i, sigma in enumerate(sigmas):\n", " tmp = pl_use_dis.compute_spectral_density(hrf_dict_pl_dis, energy_axis=np.linspace(0, 200, 201), sigma=sigma)\n", " spectral_density_pl_dis.append(tmp)" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7, 4))\n", "\n", "colors=[\n", " deep_violet,\n", " vibrant_purple,\n", " soft_coral,\n", " ocean_blue,\n", " goldenrod_yellow,\n", " emerald_green,\n", "]\n", "\n", "for i in range(len(spectral_density_pl_dis)):\n", " ax.plot(spectral_density_pl_dis[i][0], spectral_density_pl_dis[i][1], color=colors[i],\n", " label=r'$\\sigma=[%.1f, %.1f]$' % (sigmas[i][0], sigmas[i][1]))\n", "\n", "ax.legend()\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('$S(\\hbar\\omega)$ (1/meV)')\n", "ax.set_ylim([0, 0.15])\n", "ax.set_xlim([0, 200])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the HR factors, we then compute the lineshape function (or the spectral function) using the generating function approach\n", "\\begin{equation}\n", "A(\\hbar\\omega, T) = \\frac{1}{2\\pi \\hbar} \\int e^{it} G(t, T) e^{-\\frac{\\lambda|t|}{\\hbar}} \\mathrm{d}t,\n", "\\end{equation}\n", "where $\\lambda$ is the parameter describing the broadening of the zero-phonon line (ZPL)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we compute the lineshape function using the fast Fourier transform (FFT) approach. " ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998705\n" ] } ], "source": [ "linshape_fft_pl_dis = pl_use_dis.compute_lineshape_fft(hrf_dict_pl_dis, temp=4, sigma=[6, 2], zpl_broadening=0.3)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7,4))\n", "\n", "ax.plot(linshape_fft_pl_dis[0], linshape_fft_pl_dis[1], color=blue)\n", "\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('$A(\\hbar\\omega)$ (1/eV)')\n", "ax.set_ylim([0, 10])\n", "ax.set_xlim([-100, 800])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "From the lineshape function, the PL spectrum can be obtained. Compared to the lineshape, the PL spectrum includes a $(\\hbar\\omega)^3$ prefactor and is shifted to align with the ZPL.\n", "\\begin{equation}\n", "I(\\hbar\\omega) \\propto (\\hbar\\omega)^3 A(E_{\\text{ZPL}} - \\hbar\\omega, T).\n", "\\end{equation}\n", "\n", "Due to the proportionality relation, the calculation yields the relative intensity of the PL spectrum rather than its absolute intensity." ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "ezpl = 1945 # meV\n", "spectrum_pl_dis = pl_use_dis.compute_spectrum(ezpl, spectrum_type='PL', lineshape=linshape_fft_pl_dis)" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7,4))\n", "\n", "ax.plot(spectrum_pl_dis[0], spectrum_pl_dis[1], color=blue)\n", "\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('PL (arb. unit)')\n", "ax.set_xlim([1300, 2000])\n", "ax.set_ylim([0, 10])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 2. Photoluminescence spectrum from forces" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Considering the relation between atomic forces, displacements, and the Hessian within the harmonic approximation, the HR factors and the PL spectrum can also be computed from atomic forces.\n", "\n", "In this approach, we evaluate the forces on the ground-state ${}^3\\!A_2$ potential energy surface at the equilibrium geometry of the excited state ${}^3\\!E$. These forces are obtained from a single-point DFT calculation, using the input file `001_nv_diamond_abs_pl/gs_forces_at_es_coord/pw.in` and the corresponding output file `001_nv_diamond_abs_pl/gs_forces_at_es_coord/pwscf.xml`." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [], "source": [ "forces_fname = '001_nv_diamond_abs_pl/gs_forces_at_es_coord/pwscf.xml'\n", "atomic_symbols, gs_forces_es_coord = parse_forces_qexml(forces_fname)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "With the atomic forces, the mass-weighted displacement $\\Delta Q_k$ is evaluated using as\n", "\\begin{equation}\n", "\\Delta Q_k = \\frac{1}{\\omega_k^2}\\sum_{\\alpha=1}^N\\sum_{i=x,y,z}\\frac{F_{\\alpha i}e_{k, \\alpha i}}{\\sqrt{M_{\\alpha}}}.\n", "\\end{equation}\n", "Here, $F$ is the ground state forces computed at the equilibrium geometry of the excited state. Then the partial HR factors are computed as\n", "\\begin{equation}\n", "S_k = \\frac{\\omega_k \\Delta Q_k^2}{2\\hbar}\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Huang-Rhys factors using atomic forces.\n", "\n", "Total \\Delta Q is 6.457015493703e-01 amu^{0.5} \\AA\n", "Total Huang-Rhys factor is 2.942036502131e+00\n", "\n" ] } ], "source": [ "pl_using_forces = hr_solver()\n", "hrf_dict_pl_forces = pl_using_forces.compute_hrf_forces(gs_phonon_freqs, gs_phonon_modes, atomic_symbols, gs_forces_es_coord, mass_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Using the partial HR factors, we can in the same way construct the lineshape function and obtain the PL spectrum." ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998682\n" ] } ], "source": [ "lineshape_fft_pl_forces = pl_using_forces.compute_lineshape_fft(hrf_dict_pl_forces, temp=4, sigma=[6, 2], zpl_broadening=0.3)\n", "spectrum_pl_forces = pl_using_forces.compute_spectrum(ezpl, lineshape=lineshape_fft_pl_forces, spectrum_type='PL')\n" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7, 4))\n", "\n", "ax.plot(spectrum_pl_dis[0], spectrum_pl_dis[1], label='use displacements', color=blue)\n", "ax.plot(spectrum_pl_forces[0], spectrum_pl_forces[1], label='use forces', linestyle='--', color=red)\n", "\n", "ax.legend()\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('PL (arb. unit)')\n", "ax.set_xlim([1300, 2000])\n", "ax.set_ylim([0, 10])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The PL spectra obtained from the two approaches are nearly identical, indicating that the ground-state potential energy surface is well described by the harmonic approximation." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 3. Absorption spectrum from atomic displacements" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The HR theory combined with the generating function approach can also be applied to compute vibrationally resolved absorption spectra. Here, we evaluate the vibrationally resolved absorption spectrum of the ${}^3\\!A_2 \\to {}^3\\!E$ transition of the $\\text{NV}^-$ center in diamond.\n", "\n", "For this calculation, the phonon frequencies and eigenmodes of the ${}^3\\!E$ state are required, as provided in the file `001_nv_diamond_abs_pl/phonon/es_ph_mesh.hdf5`. The atomic displacements between the ${}^3\\!A_2$ and ${}^3\\!E$ states are used." ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [ "es_phonon_fname = '001_nv_diamond_abs_pl/phonon/es_ph_mesh.hdf5'\n", "es_phonon_freqs, es_phonon_modes = parse_phonopy_h5(es_phonon_fname)" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Huang-Rhys factors using atomic displacements.\n", "Total \\Delta Q is 6.529832366847e-01 amu^{0.5} \\AA\n", "Total Huang-Rhys factor is 3.102826963299e+00\n" ] } ], "source": [ "abs_use_dis = hr_solver()\n", "hrf_dict_abs_dis = abs_use_dis.compute_hrf_dis(es_phonon_freqs, es_phonon_modes, atomic_symbols, gs_coord, es_coord, cell_parameters, mass_list=mass_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can also compute the spectral density and compare with the one for PL." ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [], "source": [ "spectral_density_abs_dis = abs_use_dis.compute_spectral_density(hrf_dict_abs_dis, energy_axis=np.linspace(0, 200, 201), sigma=[6.0, 2.0])" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7, 4))\n", "\n", "ax.plot(spectral_density_abs_dis[0], spectral_density_abs_dis[1], label='Abs, use displacements', color=blue)\n", "ax.plot(spectral_density_pl_dis[3][0], spectral_density_pl_dis[3][1], label='PL, use displacements', color=red)\n", "\n", "ax.legend()\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('$S(\\hbar\\omega)$ (meV)')\n", "ax.set_xlim(0, 200)\n", "ax.set_ylim(0.0, 0.1)\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The spectral densities for absorption and PL are slightly different, reflecting the differences between the phonon modes of the ground and excited states." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We then compute the lineshape function and the corresponding absorption spectrum. Unlike the PL spectrum, the absorption spectrum includes a $(\\hbar\\omega)$ prefactor and extends toward higher energies.\n", "\\begin{equation}\n", "\\sigma(\\hbar\\omega, T) \\propto (\\hbar\\omega) A(\\hbar\\omega - E_{\\text{ZPL}}, T).\n", "\\end{equation}" ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998684\n" ] } ], "source": [ "lineshape_fft_abs_dis = abs_use_dis.compute_lineshape_fft(hrf_dict_abs_dis, temp=4, sigma=[6.0, 2.0], zpl_broadening=0.3)\n", "spectrum_abs_dis = abs_use_dis.compute_spectrum(ezpl, spectrum_type='Abs', lineshape=lineshape_fft_abs_dis)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can compare together the PL and the absorption spectra." ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7, 4))\n", "\n", "ax.plot(spectrum_abs_dis[0], spectrum_abs_dis[1], label='Absorption', color=blue)\n", "ax.plot(spectrum_pl_dis[0], spectrum_pl_dis[1], label='PL', color=red)\n", "\n", "ax.legend()\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('Absorption/PL (arb. unit)')\n", "ax.set_xlim(1500, 2400)\n", "ax.set_ylim([0, 10])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The mirror symmetry between the PL and absorption spectra does not hold strictly, due to the differences between the phonon modes of the ground and excited states and the difference in the prefactor." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## 4. Temperature-dependent photoluminescence spectrum" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Here, we use `PyPL` to compute the temperature-dependent PL spectra." ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Computing Huang-Rhys factors using atomic forces.\n", "\n", "Total \\Delta Q is 6.457015493703e-01 amu^{0.5} \\AA\n", "Total Huang-Rhys factor is 2.942036502131e+00\n", "\n" ] } ], "source": [ "temp_pl_forces = hr_solver()\n", "hrf_dict_temp_pl_forces = temp_pl_forces.compute_hrf_forces(gs_phonon_freqs, gs_phonon_modes, atomic_symbols, gs_forces_es_coord, mass_list)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "It is necessary to provide the temperature-dependent broadening parameters for the ZPL." ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998682\n", "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998682\n", "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998682\n", "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998678\n", "time_axis range: -2.067833848461893e-12 to 2.067833848461893e-12\n", "d_t (s): 2.066800448237774e-15\n", "Energy range (meV): -1000.0000000000176 to 1000.0000000000176\n", "d_E (meV): 0.9999999999998863\n", "Integral check: 999.9999999998668\n" ] } ], "source": [ "temps = [8, 150, 200, 250, 300]\n", "zpl_broadenings = [0.3, 0.8, 1.8, 3.2, 4.8]\n", "temp_pls = []\n", "\n", "for t, l in zip(temps, zpl_broadenings):\n", " tmp_lineshape = temp_pl_forces.compute_lineshape_fft(hrf_dict_temp_pl_forces, temp=t, sigma=[6.0, 2.0], zpl_broadening=l)\n", " tmp_spectrum = temp_pl_forces.compute_spectrum(ezpl, spectrum_type='PL', lineshape=tmp_lineshape)\n", " temp_pls.append(tmp_spectrum)" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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", 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" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(1, 1, figsize=(7, 6))\n", "\n", "colors=[\n", " deep_violet,\n", " vibrant_purple,\n", " soft_coral,\n", " ocean_blue,\n", " goldenrod_yellow,\n", "]\n", "\n", "for i in range(len(temps)-1, -1, -1):\n", " ax.fill_between(temp_pls[i][0], 1*i, temp_pls[i][1] + 1*i, color=colors[i],\n", " label='$T = %d$ K, $\\lambda =$ %.1f meV'%(temps[i], zpl_broadenings[i]))\n", "\n", "ax.legend(loc='upper left')\n", "ax.set_xlabel('$\\hbar\\omega$ (meV)')\n", "ax.set_ylabel('PL (arb. unit)')\n", "ax.set_xlim([1400, 2100])\n", "ax.set_ylim([0, 10])\n", "\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "As the temperature increases, the PL lineshape becomes smoother. The intensity of the phonon sideband at energies higher than the ZPL also increases, indicating that higher vibrational levels of the excited state are being populated." ] } ], "metadata": { "kernelspec": { "display_name": "Python [conda env:base] *", "language": "python", "name": "conda-base-py" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.12.7" } }, "nbformat": 4, "nbformat_minor": 4 }