KAIST

<(Back row, from left) Yeongkwan Kim, SungBin Lee, Heejun Yang, Yongsoo Yang_(Front row, from left) Jemin Park, Seokjo Hong, Jaewhan Oh>

·         Cryogenic 4D-STEM reveals how charge density waves form, fragment, and persist across a phase transition

·         First direct measurement of electronic amplitude correlations uncovers strain-driven inhomogeneity and localized order above the transition temperature

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.”

[Figure 1] Schematic illustration of an experiment employing 4D-STEM to probe the spatial variations of charge density waves in the prototypical quantum material NbSe₂ under a liquid-helium cryogenic environment (AI-generated image).

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).