DOI: 10.5281/zenodo.17420338
title: Supplementary Data Codes

description: Three-dimensional imaging of individual carbon atoms


Na Yeon Kim1*, Hanfeng Zhong1,2*, Jianhua Zhang3*, Colum M. O’Leary1*, Yuxuan Liao1, Ji Zou4, Haozhi Sha1, Minh Pham1, Weiyi Li1, Yakun Yuan1, Ji-Hoon Park5, Dennis Kim6, Huaidong Jiang3, Jing Kong5, Miaofang Chi7, Jianwei Miao1†,

1Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, CA, USA.2Department of Electrical and Computer Engineering, University of California, Los Angeles, CA, USA.3Center for Transformative Science, ShanghaiTech University, Shanghai, China.4Department of Physics, University of Basel, Basel, Switzerland.5Department of Electrical Engineering and Computer Science, Massachusetts Institute of Technology, Cambridge, MA, USA.6Department of Chemistry and Biochemistry, University of California, Los Angeles, CA, USA.7Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, TN, USA.*These authors contributed equally to this work.†Correspondence author: J.M. (j.miao@ucla.edu).



Contents




Overview

System Requirements

Repositary Contents




Overview


This repository provides all experimental and simulated data, along with source code for ptychographic and tomographic reconstruction, atom tracing, position refinement, and data analysis associated with our study. We report the first experimental determination of the 3D coordinates of individual carbon atoms with picometer-scale precision using ptychographic atomic electron tomography (pAET). Using twisted bilayer graphene as a model system, our results reveal chiral lattice distortions and interlayer interactions that were previously inaccessible to conventional microscopy. We further demonstrate the generalizability of pAET to disordered and low-Z materials through simulations on amorphous carbon and a nitrogen-vacancy center in diamond. All resources are freely available for download and unrestricted use by the research community. We hope this repository supports further advances in high-precision 3D atomic imaging.



System Requirements




Hardware Requirements


We recommend a computer with 32G DRAM, AMD Ryzen 7 6800H with Radeon Graphics 3.20 GHz CPU, and a NVIDIA GeForce RTX 3070 Ti GPU to run most data analysis source codes.



Software Requirements




OS Requirements


This package has been tested on the following Operating System:

Linux: Ubuntu 20.04.6 LTS (GNU/Linux 5.4.0-173-generic x86_64).Windows: Windows 11 Version 24H2 (OS Build 26100.3476).Mac OSX: We have not tested it on a Mac yet, but it should in principle work.



Matlab Version Requirements


This package has been tested with Matlab R2022b. All the codes have to run in their own folders. We recommend the use of Matlab version R2021a or higher to test the data and source codes.



Repositary Contents




a. Experiment Data


Folder: Measured_data

This folder contains 13 experimental projections after ptychography reconstruction and alignment as well as their corresponding angles.



b. The Extended Ptychographical Iterative Engine (EPIE) Package


Folder: EPIE_package

Run the ptychography reconstruction code Main_EPIE.m to obtain the phase retrieval projections of the twisted bilayer graphene sample.



c. The Probe REal Space Iterative REconstruction (RESIRE) Package


Folder: RESIRE_package

Run the tomography reconstruction code Main_AET_RESIRE_probe.m to obtain the 3D reconstruction of the twisted bilayer graphene sample.



d. Reconstructed 3D Volume


Folder: Final_reconstruction_volume

This folder contains the 3D volume of the twisted bilayer graphene reconstructed from Main_AET_RESIRE_probe.m.



e. Atom Tracing


Folder: Tracing_atom_position

Run the code Main_1_polynomial_tracing_iteration.m to trace the initial atomic positions from the reconstructed 3D volume. After the manual checking of the 3D atomic positions, run the code Main_2_match_atom_with_projection.m to match the traced atom with the experimental projections. This is the pre-processing step for atimic position refinement.



f. Atomic Position Refinement


Folder: Position_refinement

Run the code Main_atom_position_refinement.m to refine the 3D atomic coordinates in the twisted bilayer graphene sample.



g. Experimental Atomic Model


Folder: Final_coordinates

The final 3D atomic model and chemical element types (i.e. Carbon and Silicon) of the twisted bilayer graphene sample.



h. Match Experimental and Flat Atomic Models


Folder: Match_atom

Run the code Main_match_atom.m to match the experimental atominc model with the flat atomic model.



i. Displacement Caculation


Folder: Calculate_displacement

Run the code Main_calculate_displacement.m to obtain the displacement between the experimental atomic model and the flat atomic model.



j. Meron and Skyrmion Caculation


Folder: Calculate_Meron_Skyrmion

Run the 6 codes inside the folder Main_calculate_antimeron_lower.m, Main_calculate_antimeron_upper_1.m, Main_calculate_antimeron_upper_2.m, Main_calculate_meron_lower.m, Main_calculate_meron_upper.m, and Main_calculate_skyrmion_lower.m to obatin the merons-like and skyrmion-like structure in the experimental atomic model as well as their corresponding skyrmion number.



k. Twisted Bilayer Graphene Multislice Simulation with 64 Frozon Phonons


Folder: Twisted bilayer graphene multislice simulation with 64 frozon phonons

Run the codes inside the folder Main_1_AET_RESIRE_Probe.m, Main_2_polynomial_tracing_iteration.m, Main_3_Match_Atom_With_Position.m, and Main_4_Atom_Position_refinement.m to obatin the traced atom positions for the twisted bilayer graphene multislice simulation with 64 frozon phonons.



l. Twisted Bilayer Graphene Multislice Simulation with 32 Frozon Phonons


Folder: Twisted bilayer graphene multislice simulation with 32 frozon phonons

Run the codes inside the folder Main_1_AET_RESIRE_Probe.m, Main_2_polynomial_tracing_iteration.m, Main_3_Match_Atom_With_Position.m, and Main_4_Atom_Position_refinement.m to obatin the traced atom positions for the twisted bilayer graphene multislice simulation with 32 frozon phonons.



m. Nitrogen Vacancy Center Multislice Simulation


Folder: Nitrogen vacancy center simulation

Run the codes inside the folder Main_1_RESIRE_Multislice_With_Probe.m, Main_1_RESIRE_Multislice_Without_Probe.m, Main_1_RESIRE_Singleslice_With_Probe.m, Main_1_RESIRE_Singleslice_Without_Probe.m, Main_2_polynomial_tracing_iteration_Multislice_With_Probe.m, Main_2_polynomial_tracing_iteration_Multislice_Without_Probe.m, Main_2_polynomial_tracing_iteration_Singleslice_With_Probe.m, Main_4_Match_Atom_With_Position_Multislice.m, Main_1_RESIRE_Singleslice_With_Probe.m, Main_4_Match_Atom_With_Position_Multislice_Without_Probe.m, Main_5_Atom_Position_refinement_Multislice_With_Probe.m, and Main_5_Atom_Position_refinement_Multislice_Without_Probe.m to obatin the traced atom positions for the nitrogen vacancy center simulation.



n. Amorphous Carbon Multislice Simulation


Folder: Amorphous carbon simulation

Run the codes inside the folder Main_1_AET_RESIRE_Probe.m, Main_2_polynomial_tracing_iteration.m, Main_3_Match_Atom_With_Position.m, and Main_4_Atom_Position_refinement.m to obatin the traced atom positions for the amorphous carbon multislice simulation.



o. Resoluction Calculation


Folder: Calculate_resolution

Run the codes Main_calculate_resolution.m to calculate the resolution of the tomography reconstruction without support constraint.