Scientists capture electrons forming strange patchy patterns inside quantum materials

A research team led by Professor Yongsoo Yang of the Department of Physics at KAIST (Korea Advanced Institute of Science and Technology), working with Professors SungBin Lee, Heejun Yang, and Yeongkwan Kim and collaborators at Stanford University, has now achieved a major breakthrough. For the first time, they directly visualized how the amplitude of charge density wave order evolves across space inside a quantum material.

Nanoscale Imaging Reveals Patchy Electron Patterns

To accomplish this, the researchers used a liquid-helium-cooled electron microscope along with four-dimensional scanning transmission electron microscopy (4D-STEM). This advanced setup allowed them to track how CDW order forms, weakens, and breaks apart as temperature changes. More importantly, they were able to create detailed nanoscale maps showing not just whether electronic order is present, but how strong it is and how it connects across different regions.

The process can be compared to watching ice crystals form as water freezes, captured with extremely high magnification. In this case, however, the team observed electrons arranging themselves at temperatures near -253°C. Their microscope could resolve structures as small as one hundred-thousandth the width of a human hair. The images revealed that electronic order does not spread evenly. Some areas showed clear, well-defined patterns, while nearby regions had none at all, resembling a lake where ice forms in scattered patches rather than covering the surface all at once.

Strain and the Breakdown of Electronic Order

The study also found that these uneven patterns are closely tied to tiny distortions within the crystal. Even minute amounts of strain, far too small to detect with conventional optical methods, were enough to significantly weaken the CDW amplitude. This strong link between strain and electronic order provides direct evidence that subtle lattice distortions play a crucial role in shaping how these patterns form.

Another surprising result was the discovery that small pockets of CDW order can persist even above the transition temperature, where long-range order is typically expected to vanish. These isolated regions suggest that the transition is not a simple, uniform process. Instead of disappearing all at once, electronic order gradually loses its spatial coherence.

Measuring How Electronic Order Fades

A key achievement of the work is the first direct measurement of correlations in CDW amplitude. By examining how the strength of electronic order at one location relates to that at another, the researchers showed how coherence breaks down across the transition while local amplitude remains present. This level of detail was not accessible using traditional diffraction or scanning probe techniques.

A New Framework for Understanding Quantum Materials

Charge density waves are a fundamental feature of many quantum materials and often interact with other electronic states. By directly mapping their spatial structure and correlations, this study provides a new experimental approach for understanding how collective electronic order forms and evolves in real systems.

Dr. Yongsoo Yang emphasized the importance of the findings: "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."

The study, with Seokjo Hong, Jaewhan Oh and Jemin Park of KAIST as co-first authors, was published in Physical Review Letters.

The research 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).

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 for language editing purpose only, and the original manuscript texts were all written by human authors, not by artificial intelligence.