KAIST directly visualizes the hidden spatial order of electrons in a quantum material

Electronic order in quantum materials often emerges not uniformly, but through subtle and complex patterns that vary from place to place. One prominent example is the charge density wave (CDW), an ordered state in which electrons arrange themselves into periodic patterns at low temperatures. Although CDWs have been studied for decades, how their strength and spatial coherence evolve across a phase transition has remained largely inaccessible experimentally.

Now, a team led by Professor Yongsoo Yang of the Department of Physics at KAIST (Korea Advanced Institute of Science and Technology), together with Professors SungBin Lee, Heejun Yang, and Yeongkwan Kim, and in collaboration with Stanford University, has for the first time directly visualized the spatial evolution of charge density wave amplitude order inside a quantum material.

A New Way to See Electronic Order at the Nanoscale

Using a liquid-helium-cooled electron microscope setup combined with four-dimensional scanning transmission electron microscopy (4D-STEM), the researchers mapped how CDW order develops, weakens, and fragments as temperature changes. This approach allowed them to reconstruct nanoscale maps of the CDW amplitude, revealing not just whether the order exists, but how strong it is and how it is spatially connected.

This study is similar to filming the growth of ice crystals as water freezes using an ultra-high-magnification camera. In this case, however, the researchers observed electrons arranging themselves at cryogenic temperatures of around –253°C, and used an electron microscope capable of resolving features one hundred-thousandth the width of a human hair instead of a conventional camera. The results showed that the electronic patterns do not appear uniformly across the material. In some regions, clear patterns are visible, while in neighboring areas they are entirely absent, much like a lake that does not freeze all at once, with patches of ice interspersed with liquid water.

How Electronic Order Breaks Apart in Real Space

The team further demonstrated that this spatial inhomogeneity is closely linked to local strain inside the crystal. Even extremely small distortions that are far below optical resolution strongly suppress the CDW amplitude. This clear anticorrelation between strain and electronic order provides direct evidence that local lattice distortions play a decisive role in shaping CDW patterns.

Unexpectedly, the researchers also observed that localized regions of CDW order can persist even above the transition temperature, where long-range order is generally thought to disappear. These isolated pockets of electronic order suggest that the CDW transition is not a simple, uniform melting process, but instead involves gradual loss of spatial coherence.

A key advance of this work is the world’s first direct measurement of CDW amplitude correlations. By quantifying how the strength of electronic order at one location is related to that at another, the study reveals how CDW coherence collapses across the transition, while local amplitude remains finite. Such information could not be obtained with conventional diffraction or scanning probe techniques.

Toward a New Framework for Studying Electronic Order

Charge density waves are a central feature of many quantum materials and often coexist or compete with other electronic states. By directly accessing their spatial structure and correlations, this study provides a new experimental framework for understanding how collective electronic order forms and evolves in real materials.

Dr. Yongsoo Yang, who led the research, explained the significance of the results: “Until now, the spatial coherence of charge density waves was largely inferred indirectly. Our approach allows us to directly visualize how electronic order varies across space and temperature, and to identify the factors that locally stabilize or suppress it.”

This research, with Seokjo Hong, Jaewhan Oh and Jemin Park of KAIST as co-first authors, was published online in Physical Review Letters on January 6th (Title: Spatial correlations of charge density wave order across the transition in 2H-NbSe₂).

The study was mainly supported by the National Research Foundation of Korea (NRF) Grants (Individual Basic Research Program, Basic Research Laboratory Program, Nanomaterial Technology Development Program) funded by the Korean Government (MSIT).

Paper Title: Spatial correlations of charge density wave order across the transition in 2H-NbSe₂

Authors: Seokjo Hong, Jaewhan Oh, Jemin Park, Woohyun Cho, Soyoung Lee, Colin Ophus, Yeongkwan Kim, Heejun Yang, SungBin Lee, and Yongsoo Yang

Journal: Physical Review Letters

DOI: https://doi.org/10.1103/776d-dnmf

Date: January 6, 2026

Contact Number: +82-42-350-7303

e-mail: yongsoo.yang@kaist.ac.kr

Lab: Multi-Dimensional Atomic Imaging Laboratory (MDAIL) at KAIST ( https://mdail.kaist.ac.kr/ )

Keywords:

Charge density wave
NbSe2

4D-STEM

Spatial correlation

CDW-strain anticorrelation

Acknowledgements:

The authors thank E.-G. Moon for helpful discussions. This research was mainly supported by the National Research Foundation of Korea (NRF) Grants (RS-2023-00208179 and RS-2025-02243032) funded by the Korean Government (MSIT). Y.Y. also acknowledges the support from the KAIST singularity professor program. S.B.L. was supported by NRF Grant (2021R1A2C109306013) and Nano Material Technology Development Program through the NRF funded by MSIT (RS-2023-00281839). Y.K. was financially supported by NRF Grant (No. RS-2022-00143178 and No. RS-2024-00345856) and Korea Research Institute of Standards and Science (KRISS) (Grant No. KRISS-GP2025-0015). H. Y. was supported by an NRF Grant No. RS-2024-00340377 funded by MSIT. The 4D-STEM, ADF-STEM and EELS experiments were conducted using a double Cs corrected Titan cubed G2 60-300 (FEI) and Spectra Ultra (ThermoFisher) equipment at KAIST Analysis Center for Research Advancement (KARA). Excellent support by Hyung Bin Bae, Jin-Seok Choi and the staff of KARA is gratefully acknowledged. We declare that the authors utilized the ChatGPT (https://chat.openai.com/chat) for language editing purpose only, and the original manuscript texts were all written by human authors, not by artificial intelligence.