DOI: 10.5281/zenodo.17823449
title: Spatial correlations of charge density wave order across the transition in 2H-NbSe2

description: Data and Source Codes

The data and source codes for the paper [S. Hong, J. Oh, J. Park, W. Cho, S. Lee, C. Ophus, Y. Kim, H. Yang, SB. Lee and Y. Yang, "Spatial correlations of charge density wave order across the transition in 2H-NbSe2", Phys. Rev. Lett. 136,_016504 (2026).] are posted below.

 

Overview

Charge density waves (CDWs) involve coupled amplitude and phase degrees of freedom, but direct access to local amplitude correlations remains experimentally challenging. Here, we report cryogenic four-dimensional scanning transmission electron microscopy (4D-STEM) measurements of CDW ordering in a 2H-NbSe2 flake of 24 nm thickness, enabled by liquid helium-based cooling. By mapping the spatial distribution of CDW superlattice intensities at nanometer-scale resolution and analyzing their autocorrelations, we extract the temperature-dependent correlation length associated with the local amplitude of the CDW order parameter, independent of global phase coherence. Our results reveal that a finite local CDW amplitude is already established well above the transition temperature. When the system is cooled below the transition temperature down to 20 K, the correlation length extends to nearly 110 nm, and the local CDW amplitude is found to strongly anticorrelate with the local strain field.

 



System Requirements


1. All software dependencies and operating systems (including version numbers)

Software: MATLAB R2023a – academic use

Operating systems: Windows 10

 

2. Versions the software has been tested on

MATLAB R2023a – academic use

 

3. Any required non-standard hardware

There are no non-standard hardware

 



Repositary Contents


1. Raw 4D-STEM Data

The raw 4D-STEM dataset of 2H-NbSe2 flake specimen, after 4x4 real-space binning. Measured at multiple base temperatures of 20K, 25K, 27K, 29K, 31K, 33K, 35K, 37K, 40K, 45K, and 300K.

 

This folder contains raw experimental 4D-STEM dataset of 2H-NbSe2 flake specimen after 4x4 real-space binning. The filename represents the base temperature at which the 4D-STEM data was collected.

 

File name

Data_XXK.mat  -   experimental 4D-STEM dataset for XX K temperature.

 

 

Pre-determined lists of CDW peak positions (multiple of 1/3s) visible in the detetor field of view were utilized during the data analysis, and they are also supplied together in the folder.

 



File name

SpanSuperVecList_OldInd.mat    -   pre-determined list of CDW peak positions (multiple of 1/3s) visible in the detetor field of view

SpanSuperVecList_NewInd.mat   -  pre-determined list of CDW peak positions (multiple of 1/3s) visible in the detetor field of view, consistent with the indexing used in the published paper.

 

 




2. Data analysis Codes

File: Analysis_Codes.zip

 

This zip file contains the MATLAB code for CDW peak intensity, correlation length and strain analysis.

 

1) Plotting averaged diffraction parttern

run Averaged_dffraction_pattern_export_forFigure2.m    

- For obtaining diffraction patterns averaged over real-space probe positions

- This reproduces Figure 2 of the published paper.

 

2) CDW peak intensity analysis 

run Analysis_Peak_Signal_Background.m 

-for analyzing CDW peak positions and the integrated peak intensity, integrated background intensity for each peak for each

 



3) CDW order parameter map analysis

run Analysis_Order_Parameter_Map_Figure3.m  

- For obtining the CDW peak intensity (order parameter) map in real space across the measured temperatures, based on the integrated peak intensity, integrated background intensity.

- This reproduces Figure 3 of the published paper.

 



4) CDW autocorrelation and correlation length analysis

run Analysis_Autocorrelations_Figure4.m

- For performing the autocorrelation and correlation length analysis for CDW amplitude. 

- This reproduces Figure 4 of the published paper.

 



5) NbSe2 integer diffraction peak position analysis 

run Analysis_Peak_Positions_for_Strain.m

- For analyzing NbSe2 integer diffraction peak positions for strain analysis.

 



6) Strain map analysis

run Analysis_Strain_Calculation_Figure5.m

- For obtining the strain map of the 4D-STEM scanned region across the measured temperatures based on the NbSe2 integer diffraction peak positions.

- This reproduces Figure 5 of the published paper.





 

* sub-functions utilized in the codes above:

calc_gauss2D_PD.m

fit_gauss2D_PD.m

My_binning.m

My_paddzero.m

 



Additional Notes


If you use any of the above data or source codes in your publications and/or presentations, our paper should be properly cited: S. Hong, J. Oh, J. Park, W. Cho, S. Lee, C. Ophus, Y. Kim, H. Yang, SB. Lee and Y. Yang, "Spatial correlations of charge density wave order across the transition in 2H-NbSe2",  Phys. Rev. Lett. 136, 016504 (2026).

If you have any questions regarding the above data or source codes, please contact Yongsoo Yang, Department of Physics, Korea Advanced Institute of Science and Technology (KAIST), Daejeon 34141, Korea. Email: yongsoo.yang@kaist.ac.kr .

 



The code is distributed under the terms of the GNU General Public License v3.0 (GPL-3.0).