{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Sewing band structure by subduced representation" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Load modules and prepare functions" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "spgrep_modulation==0.1.dev33+gc7ed76b.d20220823\n", "phonopy==2.16.3\n" ] } ], "source": [ "from __future__ import annotations\n", "\n", "from pathlib import Path\n", "import warnings\n", "from itertools import product\n", "from dataclasses import dataclass\n", "\n", "import matplotlib.pyplot as plt\n", "import seaborn as sns\n", "\n", "import phonopy\n", "import seekpath\n", "import numpy as np\n", "import networkx as nx\n", "\n", "import spgrep_modulation\n", "from spgrep.group import get_little_group\n", "from spgrep.representation import get_character\n", "from spgrep_modulation.modulation import Modulation\n", "\n", "%matplotlib inline\n", "\n", "print(f\"spgrep_modulation=={spgrep_modulation.__version__}\")\n", "print(f\"phonopy=={phonopy.__version__}\")" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "sns.set_context(\"poster\")\n", "warnings.simplefilter(\"ignore\")" ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "@dataclass\n", "class BandNode:\n", " \"\"\"Each point in band structure, characterized by eigenvalue and character of irrep.\"\"\"\n", "\n", " qpoint: NDArrayFloat\n", " character: NDArrayComplex\n", " eigenvalue: float\n", " frequency: float\n", " degeneracy: int\n", "\n", "\n", "@dataclass\n", "class QpointInfo:\n", " \"\"\"Container for little co-group at qpoint.\"\"\"\n", "\n", " qpoint: NDArrayFloat\n", " little_rotations: NDArrayInt\n", " little_translations: NDArrayFloat\n", " nodes: list[BandNode]\n", "\n", " @classmethod\n", " def from_modulation(cls, md: Modulation):\n", " nodes = []\n", " for eigenvalue, _, irrep in md.eigenspaces:\n", " degeneracy = irrep.shape[1]\n", " character = get_character(irrep)\n", " nodes.append(\n", " BandNode(\n", " qpoint=md.qpoint,\n", " character=character,\n", " eigenvalue=eigenvalue,\n", " frequency=md.eigvals_to_frequencies(eigenvalue),\n", " degeneracy=degeneracy,\n", " )\n", " )\n", "\n", " return cls(\n", " qpoint=md.qpoint,\n", " little_rotations=md.little_rotations,\n", " little_translations=md.little_translations,\n", " nodes=nodes,\n", " )\n", "\n", "\n", "def enumerate_non_overlapped_paths(\n", " adj_: dict[Any, list[Any]], source: Any, destination: Any\n", ") -> list[list[Any]]:\n", " adj = adj_.copy()\n", " all_paths = []\n", " while len(adj[source]) > 0:\n", " path = []\n", " head = source\n", " while (head != destination) and (len(adj[head]) > 0):\n", " path.append(head)\n", " head = adj[head].pop()\n", " all_paths.append(path[1:]) # Ignore source\n", "\n", " return all_paths\n", "\n", "\n", "def _saw_consecutive(\n", " qpoint_info1: QpointInfo,\n", " qpoint_info2: QpointInfo,\n", " num_atoms: int,\n", " decimals=3,\n", ") -> list[tuple[int, int]]:\n", " \"\"\"Connect nodes in consecutive qpoints.\n", "\n", " Assume little group of `qpoint_info1` includes little group of `qpoint_info2`.\n", "\n", " Parameters\n", " ----------\n", " qpoint_info1: QpointInfo\n", " qpoint_info2: QpointInfo\n", "\n", " Returns\n", " -------\n", " connections:\n", " Let `connections[i] = (n1, n2)`. `qpoint_info1.nodes[n1]` and `qpoint_info2.nodes[n2]` are connected.\n", " \"\"\"\n", " graph = nx.DiGraph()\n", " num_nodes1 = len(qpoint_info1.nodes)\n", " num_nodes2 = len(qpoint_info2.nodes)\n", " graph.add_nodes_from(range(num_nodes1))\n", " graph.add_nodes_from(range(num_nodes1, num_nodes1 + num_nodes2))\n", "\n", " # Retrieve subgroup of little co-group at qpoint-1 preserving qpoint2\n", " _, _, mapping = get_little_group(\n", " rotations=qpoint_info1.little_rotations,\n", " translations=qpoint_info1.little_translations,\n", " kpoint=qpoint_info2.qpoint,\n", " )\n", "\n", " for idx1, node1 in enumerate(qpoint_info1.nodes):\n", " subduced_character1 = node1.character[mapping]\n", " for offset, node2 in enumerate(qpoint_info2.nodes):\n", " idx2 = num_nodes1 + offset\n", " count = np.sum(np.conj(subduced_character1) * node2.character) / len(mapping)\n", " count = np.around(np.real(count)).astype(int)\n", " if count >= 1:\n", " # Work around to stop min-cost-flow algorithm\n", " weight = abs(node1.eigenvalue - node2.eigenvalue)\n", " weight = int(weight * (10**decimals))\n", " capacity = min([node1.degeneracy, node2.degeneracy, count])\n", " graph.add_edge(idx1, idx2, weight=weight, capacity=capacity)\n", "\n", " # Add source and destination to solve as min-cost flow\n", " source = num_nodes1 + num_nodes2\n", " destination = source + 1\n", " demand = 3 * num_atoms # Number of branches\n", " graph.add_node(source, demand=-demand)\n", " graph.add_node(destination, demand=demand)\n", " for idx1, node1 in enumerate(qpoint_info1.nodes):\n", " graph.add_edge(source, idx1, weight=0, capacity=node1.degeneracy)\n", " for offset, node2 in enumerate(qpoint_info2.nodes):\n", " idx2 = num_nodes1 + offset\n", " graph.add_edge(idx2, destination, weight=0, capacity=node2.degeneracy)\n", "\n", " assert sum([node.degeneracy for node in qpoint_info1.nodes]) == demand\n", " assert sum([node.degeneracy for node in qpoint_info2.nodes]) == demand\n", " flowdict = nx.min_cost_flow(graph)\n", "\n", " # Recover matching\n", " active_edges = {}\n", " for src, dst_flow in flowdict.items():\n", " for dst, flow in dst_flow.items():\n", " if src in active_edges:\n", " active_edges[src].extend([dst for _ in range(flow)])\n", " else:\n", " active_edges[src] = [dst for _ in range(flow)]\n", " all_paths = enumerate_non_overlapped_paths(active_edges, source, destination)\n", "\n", " connections = []\n", " for idx1, idx2 in all_paths:\n", " connections.append((idx1, idx2 - num_nodes1))\n", " return connections\n", "\n", "\n", "def sew_bands(\n", " ph: phonopy.Phonopy,\n", " start: list[float],\n", " stop: list[float],\n", " num: int = 17,\n", "):\n", " \"\"\"Connect bands between qpoints `start` and `stop`.\n", "\n", " Returns\n", " -------\n", " list_qpoint_info: list[QpointInfo]\n", " connections: list[list[tuple[int, int]]]\n", " list with length = 3 * len(ph.primitive)\n", " connections[k] is the k-th band composed of list of tuples `(i, idx)` corresponding to `list_qpoint_info[i].nodes[idx]`\n", " ratios: array with shape (num, )\n", " \"\"\"\n", " if num <= 2:\n", " raise ValueError(\"Specify more than three points for `num`.\")\n", "\n", " list_qpoint_info = []\n", " ratios = np.linspace(0, 1, num=num, endpoint=True)\n", " for ratio in ratios:\n", " qpoint = np.array(start) * (1 - ratio) + np.array(stop) * ratio\n", " md = Modulation.with_supercell_and_symmetry_search(\n", " dynamical_matrix=ph.dynamical_matrix,\n", " supercell_matrix=[1, 1, 1], # No need to care about being commensurate here\n", " qpoint=qpoint,\n", " factor=ph.unit_conversion_factor,\n", " )\n", " info = QpointInfo.from_modulation(md)\n", " list_qpoint_info.append(info)\n", "\n", " # Connect between consecutive qpoints\n", " all_paths = []\n", " num_atoms = len(ph.primitive)\n", " for i in range(num - 2):\n", " for n1, n2 in _saw_consecutive(list_qpoint_info[i], list_qpoint_info[i + 1], num_atoms):\n", " all_paths.append(((i, n1), (i + 1, n2)))\n", " for n2, n1 in _saw_consecutive(list_qpoint_info[-1], list_qpoint_info[-2], num_atoms):\n", " # Reverse the last path\n", " all_paths.append(((num - 2, n1), (num - 1, n2)))\n", "\n", " adj = {}\n", " for i, info in enumerate(list_qpoint_info):\n", " for idx in range(len(info.nodes)):\n", " adj[(i, idx)] = []\n", " for src, dst in all_paths:\n", " adj[src].append(dst)\n", "\n", " # Add dummy source and destination nodes\n", " source = \"source\"\n", " destination = \"destination\"\n", " adj[source] = []\n", " adj[destination] = []\n", " for idx, node in enumerate(list_qpoint_info[0].nodes):\n", " adj[source].extend([(0, idx) for _ in range(node.degeneracy)])\n", " for idx, node in enumerate(list_qpoint_info[-1].nodes):\n", " adj[(num - 1, idx)].extend([destination for _ in range(node.degeneracy)])\n", "\n", " connections = enumerate_non_overlapped_paths(adj, source, destination)\n", " return list_qpoint_info, connections, ratios" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Prepare `Phonopy` object" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "path = Path().resolve().parent.parent / \"tests\" / \"phonopy_mp-661.yaml.xz\"\n", "ph = phonopy.load(path)\n", "ph.auto_band_structure(plot=True).show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Sewing" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [], "source": [ "band_path = seekpath.get_path(ph.primitive.totuple())\n", "label1, label2 = band_path[\"path\"][0]\n", "list_qpoints_info, connections, ratios = sew_bands(\n", " ph, band_path[\"point_coords\"][label1], band_path[\"point_coords\"][label2], num=512\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Plot band structure with connection\n", "\n", "Yellow and light blue branches seem to be mis-identified.\n", "They have the equivalent irreps between Gamma and M points.\n", "Thus, there is no way to distinguish them only from symmetry." ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0, 0, 'GAMMA'), Text(1, 0, 'M')]" ] }, "execution_count": 6, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6.75, 6.75 * 1.6))\n", "for i, (connection, ratio) in enumerate(zip(connections, ratios)):\n", " color = f\"C{i}\"\n", " frequencies = [\n", " list_qpoints_info[qpoint_idx].nodes[band_idx].frequency\n", " for (qpoint_idx, band_idx) in connection\n", " ]\n", " ax.plot(ratios[1:], frequencies[1:], color=color)\n", "\n", "ax.set_xlabel(\"Wave vector\")\n", "ax.set_ylabel(\"Frequency (THz)\")\n", "ax.set_xticks([0, 1])\n", "ax.set_xticklabels([label1, label2])" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[Text(0, 0, 'GAMMA'), Text(1, 0, 'M')]" ] }, "execution_count": 8, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "fig, ax = plt.subplots(figsize=(6.75, 6.75 * 1.6))\n", "for i, (connection, ratio) in enumerate(zip(connections, ratios)):\n", " color = f\"C{i}\"\n", " frequencies = [\n", " list_qpoints_info[qpoint_idx].nodes[band_idx].frequency\n", " for (qpoint_idx, band_idx) in connection\n", " ]\n", " # ax.plot(ratios[1:], frequencies[1:], color=color)\n", " ax.scatter(ratios[1:], frequencies[1:], color=color, s=1)\n", "\n", "ax.set_xlabel(\"Wave vector\")\n", "ax.set_ylabel(\"Frequency (THz)\")\n", "ax.set_xticks([0, 1])\n", "ax.set_ylim(11.8, 12.8)\n", "ax.set_xticklabels([label1, label2])" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] } ], "metadata": { "kernelspec": { "display_name": "Python 3.10.4 ('spgrep')", "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": "3.10.4" }, "orig_nbformat": 4, "vscode": { "interpreter": { "hash": "88c77d0dd5409a9a505b149d1d516cb944fb2ee79f549abf35dc2e7bd6c12498" } } }, "nbformat": 4, "nbformat_minor": 2 }