A new imaging technique uncovers how electronic patterns in quantum materials evolve unevenly across space and temperature.
Electronic order inside quantum materials does not always unfold in a smooth or predictable way. Instead, it can break into intricate, patch-like patterns that shift across space. A classic example is the charge density wave (CDW), where electrons settle into repeating arrangements at low temperatures. Despite decades of research, scientists have struggled to directly observe how these patterns strengthen, fade, and lose coordination during phase transitions.
Now, researchers led by Professor Yongsoo Yang at KAIST (Korea Advanced Institute of Science and Technology), working with colleagues including Professors SungBin Lee, Heejun Yang, Yeongkwan Kim, and collaborators at Stanford University, have captured this process in unprecedented detail.
Their work provides a real-space view of how electronic order evolves inside a quantum material, offering a clearer picture of behavior that was previously inferred only indirectly.
A New Way to See Electronic Order at the Nanoscale
The researchers used a liquid helium cooled electron microscope together with four-dimensional scanning transmission electron microscopy (4D-STEM) to follow how CDW order forms, weakens, and breaks apart as temperature varies. This method produced detailed nanoscale maps that show not only where CDW order exists, but also how strong it is and how different regions connect to one another.
The process can be compared to recording ice crystals forming as water freezes with an extremely powerful camera. In this experiment, however, electrons were observed arranging themselves at about –253°C (–423°F), using an instrument capable of resolving features about one hundred thousand times smaller than the width of a human hair.
The images reveal that these electronic patterns are not evenly distributed. Some areas show clear, well-defined structures, while nearby regions show none, similar to a lake that freezes unevenly, leaving patches of ice mixed with liquid water.
How Electronic Order Breaks Apart in Real Space
The team found that this patchy behavior is strongly tied to local strain within the crystal. Even extremely small distortions, too subtle to detect with optical methods, can significantly weaken the CDW signal. This inverse relationship between strain and electronic order shows that tiny lattice changes play a major role in shaping these patterns.
The researchers also discovered that small pockets of CDW order can remain even above the transition temperature, where long-range order is expected to vanish. This suggests that the transition does not occur all at once but instead involves a gradual loss of coordination across the material.
Another major achievement is the first direct measurement of correlations in CDW amplitude. By examining how the strength of electronic order at one point relates to another, the study shows how overall coherence breaks down while local order persists. Traditional diffraction and scanning probe methods could not provide this level of detail.
Toward a New Framework for Studying Electronic Order
Charge density waves are a key feature in many quantum materials and often interact with other electronic states. By directly mapping their spatial structure and correlations, this work introduces a new way to study how collective electronic behavior forms and changes in real systems.
Dr. Yongsoo Yang, who led the study, highlighted its importance: “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.”
Reference: “Spatial Correlations of Charge Density Wave Order across the Transition in 2H−NbSe2” by Seokjo Hong, Jaewhan Oh, Jemin Park, Woohyun Cho, Soyoung Lee, Colin Ophus, Yeongkwan Kim, Heejun Yang, SungBin Lee and Yongsoo Yang, 6 January 2026, Physical Review Letters.
DOI: 10.1103/776d-dnmf
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).
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