University of Wisconsin-Madison engineers have developed a new technique to map the quantum phase diagram in a promising class of quantum materials called Weyl semimetals by tracking “hotspots” in an unusual quantum phenomenon called the nonlinear Hall effect.
The technique, based on a unique quantum geometry signature, enables scientists to identify phase transitions in topological materials and determine whether these transitions are linked to deeper changes in the material’s topological properties. This insight could accelerate the discovery of exotic quantum phases and help identify materials with optimal electronic characteristics for building next-generation low-power, high-efficiency electronics and optoelectronic devices.
The research, led by Ying Wang, an assistant professor in electrical and computer engineering at UW-Madison, appeared July 10, 2025, in the journal Nature Communications. Daniel Rhodes and Jun Xiao, assistant professors in materials science and engineering at UW-Madison, collaborated on the research.
Topological materials are a class of quantum materials whose electronic behavior is governed not only by local atomic arrangements but also by global topological properties of their quantum wavefunctions. Unlike conventional materials (insulators, metals, and semiconductors), electrons in topological materials flow along the surface and edges of a material and will maintain their movement pattern despite any twists, turns or other obstructions they may encounter. Over the last two decades, researchers have begun engineering topological materials for use in robust and low-power electronics and even topological quantum computing.
Among those materials, topological semimetals stand out for their unusual electronic behavior—electrons can flow in these materials with little resistance and behave as if they were massless particles. But some of the most exciting possibilities arise when these topological effects interact with strong electron interactions, giving rise to novel phases of matter like charge density waves or even topological superconductivity.
Understanding this interplay between topology and electron correlation is a major frontier in quantum materials and engineering. Yet, experimentally probing these complex quantum states is challenging, often requiring multiple types of measurements and difficult-to-interpret signals.
To tackle this, the UW–Madison team turned to the nonlinear Hall effect, a recently discovered quantum electrical response that is sensitive to both symmetry and topology, as a window into the underlying physics. Their goal was to determine whether this nonlinear signal could act as an electrical fingerprint for hidden phase transitions and emergent quantum states in a topological semimetal called tantalum iridium telluride (TaIrTe₄), especially in its “few-layer” form, just several layers of atoms thick.
By carefully varying the temperature and input current, the researchers observed dramatic changes in the nonlinear Hall signal. In particular, they found that the nonlinear Hall response was 350 times stronger at 2 Kelvin (about –450 °F) compared to room temperature—a clear sign of an emergent quantum phase.
Further investigation revealed that this enhanced response coincided with the appearance of a charge density wave (CDW)—a type of ordered electron state known to reshape the electronic structure of materials. Using their home-built Raman spectrometer, the team confirmed that a new charge density wave phase emerged in the low-temperature regime, likely causing the nonlinear enhancement. With this information, the researchers constructed a quantum phase diagram for ultrathin tantalum iridium telluride—mapping how temperature and current drive the formation of correlated quantum states.
“This work suggests this method could be used as a phase diagram probe,” says Wang. “If you find hotspots in the nonlinear Hall effect, it could indicate that a new quantum state is emerging.”
Importantly, the charge density wave discovered in the few-layer tantalum iridium telluride exhibited record-high nonlinear conductivity, making it a strong candidate for applications such as nonlinear optoelectronics and quantum energy harvesting.
While tantalum iridium telluride shows remarkable electronic behavior, it comes with challenges—chemical instability under ambient conditions. Wang and her collaborators are working to improve its stability and identify other Weyl semimetals with similar properties but better environmental resilience.
Building on this research, Wang is working on a longer-term project investigating how topological semimetals interact with radio frequencies signals such as Wi-Fi. Her vision is to engineer quantum materials that can harvest ambient electromagnetic energy while maintaining compatibility with modern chip technologies. “I think a chemically stable topological semimetal material with large nonlinearity would be suited for integration with CMOS, or computer chip, fabrication techniques,” she says. “Our new probe could guide us to find it.”
Ying Wang is the Dugald C. Jackson Assistant Professor in electrical and computer engineering at UW-Madison.
Other UW-Madison authors include Haotian Jiang, Tairan Xi, Yangchen He, Hongrui Ma, and Yulu Mao.
Other authors include Jiangxu Li and Yang Zhang of the University of Tennessee, Knoxville, and Takashi Taniguchi and Kenji Watanabe of the National Institute for Materials Science, Tsukuba, Japan.
The authors acknowledge support from the Department of Energy Office of Basic Energy Sciences through grant DE-SC0024176; the Office of Naval Research through contract No. N00014-24−1−2068; National Science Foundation through the University of Wisconsin Materials Research Science and Engineering Center under grant No. DMR-2309000.
Featured image caption: Ying Wang working in her lab. Credit: Joel Hallberg.