Electron ordering mapped in quantum material with cryogenic 4D-STEM

by Riko Seibo
Tokyo, Japan (SPX) Jan 20, 2026

Electronic order in quantum materials often arises through intricate, non-uniform patterns that shift across space. A well-known example is the charge density wave (CDW), an ordered electronic state that forms periodic patterns at low temperatures. Although CDWs have been studied for decades, directly observing how their strength and spatial coherence evolve through a phase transition has remained an experimental challenge.

A research team led by Professor Yongsoo Yang from the Department of Physics at KAIST, in collaboration with Professors SungBin Lee, Heejun Yang, and Yeongkwan Kim and colleagues at Stanford University, has now directly visualized how CDW amplitude order develops and changes inside a quantum material for the first time.

Mapping Electronic Order in Real Space

Using a liquid-helium-cooled electron microscope and four-dimensional scanning transmission electron microscopy (4D-STEM), the researchers traced how CDW order grows, weakens, and fragments as temperature varies. This technique enabled nanoscale mapping of CDW amplitude, revealing not only where the order exists but also its strength and connectivity.

The process is akin to filming the freezing of a lake - where some areas ice over first while others remain liquid. Here, the team observed electrons self-organizing at cryogenic temperatures near -253 C, resolving details more than 100,000 times smaller than the width of a human hair. The resulting maps revealed that CDW order forms inhomogeneously across the crystal, with well-ordered regions interspersed with disordered ones.

Linking Local Strain to Electronic Order

The researchers further showed that local strain strongly influences CDW formation. Even minute crystal distortions - too small to detect optically - were found to suppress CDW amplitude. This clear anticorrelation between strain and electronic order demonstrates the decisive role of lattice imperfections in shaping electronic behavior.

Intriguingly, localized CDW regions persisted even above the nominal transition temperature, where long-range order is expected to melt. These residual pockets indicate that CDW transitions occur gradually rather than abruptly, through partial loss of spatial coherence.

A New Approach to Quantum Material Studies

Crucially, the study reports the first direct measurement of CDW amplitude correlations, revealing how coherence deteriorates across the transition while local order remains finite. This level of detail was previously inaccessible with traditional diffraction or scanning probe methods.

Since CDWs often coexist or compete with other electronic states, this framework offers a new route to investigate how collective electronic order emerges and evolves in real space.

As Dr. Yang explains, "Until now, the spatial coherence of charge density waves was largely inferred indirectly. Our approach allows us to directly see how electronic order changes across both space and temperature, and to pinpoint the factors that stabilize or disrupt it."

The research - conducted with Seokjo Hong, Jaewhan Oh, and Jemin Park of KAIST as co-first authors - was published in Physical Review Letters on January 6, under the title "Spatial correlations of charge density wave order across the transition in 2H-NbSe2."

Funding was provided by the National Research Foundation of Korea (NRF) through the Individual Basic Research, Basic Research Laboratory, and Nanomaterial Technology Development programs under the Korean Government (MSIT).

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