DOI: 10.5061/dryad.n02v6wxbd
title: Data from: Quantized crystalline-electromagnetic responses in insulators

description: We introduce new classes of gapped topological phases characterized by
 quantized crystalline-electromagnetic responses, termed "multipolar
 Chern insulators". These systems are characterized by nonsymmorphic
 momentum-space symmetries and mirror symmetries, leading to quantization
 of momentum-weighted Berry curvature multipole moments. We construct
 lattice models for such phases and confirm their quantized responses
 through numerical calculations. These systems exhibit bound charge and
 momentum densities at lattice and magnetic defects, and currents induced
 by electric or time-varying strain fields. Our work extends the
 classification of topological matter by uncovering novel
 symmetry-protected topological phases with quantized responses. The data
 for reproducing the figures in the main text and supplemental material of
 the article 'Quantized crystalline-electromagnetic responses in
 insulators.'
description: # Data from: Quantized crystalline-electromagnetic responses in insulators
 Dataset DOI:
 [10.5061/dryad.n02v6wxbd](https://doi.org/10.5061/dryad.n02v6wxbd) ##
 Description of the data and file structure This repository contains the
 numerical data used to reproduce the figures in the associated
 manuscript.\ All files are provided as plain text (`.txt`) tables. The
 file names correspond directly to the figure numbers in the main text or
 the Supplemental Material (SM). ### Files and variables ## File Overview
 ### **Main Text Figures** * **fig2d_(main_text).txt** * File description:
 Data used to generate **Figure 2d**. * Figure description: Plot showing
 the linear response of charge density bound to translation flux for the
 topological phases (with Berry curvature dipole moment, *D~y~* = π, 2π)
 and trivial phase (with *D~y~* = 0) in the dipolar Chern insulator model.
 * **fig3d_(main_text).txt** * File description: Data used to generate
 **Figure 3d**. * Figure description: Plot showing the linear response of
 the momentum polarization to the lattice shear for the topological phase
 (*Q~xy~* = 2π^2^) and trivial phase (*Q~xy~* = 0) in the quadrupolar Chern
 insulator model. ### **Supplemental Material Figures** *
 **figS2a_(SM).txt** * File description*:* Data used to generate **Figure
 S2a**. * Figure description*:*  Energy dispersion for the dipolar Chern
 insulator model with mass term, M = 2, and open boundary conditions along
 x, showing the presence of bidirectional edge states.  *
 **figS2b_(SM).txt** * File description*:* Data used to generate **Figure
 S2b**. * Figure description*:* Energy dispersion for the quadrupolar Chern
 insulator model with mass term, M = 1, and open boundary conditions along
 x, showing the presence of bidirectional edge states. *
 **figS3a_M_0_(SM).txt, figS3a_M_2_(SM).txt, figS3a_M_4_(SM).txt** * File
 description*:* Data for **Figure S3a** for **M = 0, 2, 4**. * Figure
 description*:* Effect of hopping disorder on the quantization of responses
 in the dipolar Chern insulator model for phases obtained at various values
 of the mass term, M = 0, 2, 4. *
 **figS3b_M_0_(SM).txt, figS3b_M_2_(SM).txt, figS3b_M_4_(SM).txt** * File
 description*:* Data for **Figure S3b** for **M = 0, 2, 4**. * Figure
 description*:* Effect of strain disorder on the quantization of responses
 in the dipolar Chern insulator model for phases obtained at various values
 of the mass term, M = 0, 2, 4. * **figS4a_(SM).txt** * File description:
 Data used to generate **Figure S4a**. * Figure description*:* Effects of
 symmetry breaking on the quantization of *Q~ij~*. * **figS4b_(SM).txt** *
 File description: Data used to generate **Figure S4b**. * Figure
 description*:* Effects of symmetry breaking on the quantization of
 *Q~ij~*. * **figS5a_(SM).txt** * File description: Data used to generate
 **Figure S5a**. * Figure description*:* Effects of symmetry breaking on
 the quantization of *D~i~*. * **figS5b_(SM).txt** * File description: Data
 used to generate **Figure S5b**. * Figure description*:* Effects of
 symmetry breaking on the quantization of *D~i~*.