Mapping the geometry of quantum worlds: measuring the quantum geometric tensor in solids.
Quantum states are like complex shapes in a hidden world, and understanding their geometry is key to unlocking the mysteries of modern physics. One of the most important tools for studying this geometry is the quantum geometric tensor (QGT). This mathematical object reveals how quantum states “curve” and interact, shaping phenomena ranging from exotic materials to groundbreaking technologies.
The QGT has two parts, each with distinct significance:
1. The Berry curvature (the imaginary part): This governs topological phenomena, such as unusual electrical and magnetic behaviors in advanced materials.
2. The quantum metric (the real part): Recently gaining attention, this influences surprising effects like flat-band superfluidity, quantum Landau levels, and even the nonlinear Hall effect.
While the QGT is crucial for understanding these phenomena, measuring it directly has been a challenge, previously limited to simple, artificial systems.
A breakthrough now allows scientists to measure the QGT in real crystalline solids. Using an advanced technique involving polarization-, spin-, and angle-resolved photoemission spectroscopy, researchers have reconstructed the QGT in a material called CoSn, a “kagome metal” with unique quantum properties like topological flat bands. This metal forms patterns resembling a woven basket, hosting quantum effects that were previously only theorized.
This new method of studying the QGT—capturing its structure in both momentum and energy—offers a revolutionary way to explore quantum geometric phenomena in natural materials. It could pave the way for innovations in quantum electronics, magnetism, and energy systems, bringing us closer to harnessing the full potential of the quantum world.
The COVID pandemic, too, had an impact. Kang, who is from South Korea, was based in that country during the pandemic. “That facilitated a collaboration with theorists in South Korea,” says Kang, an experimentalist.
The pandemic also led to an unusual opportunity for Comin. He traveled to Italy to help run the ARPES experiments at the Italian Light Source Elettra, a national laboratory. The lab was closed during the pandemic, but was starting to reopen when Comin arrived. He found himself alone, however, when Kang tested positive for COVID and couldn’t join him. So he inadvertently ran the experiments himself with the support of local scientists. “As a professor, I lead projects but students and postdocs actually carry out the work. So this is basically the last study where I actually contributed to the experiments themselves,” he says with a smile.
In addition to Kang and Comin, additional authors of the Nature Physics paper are Sunje Kim of Seoul National University (Kim is a co-first author with Kang); Paul M. Neves, a graduate student in the MIT Department of Physics; Linda Ye of Stanford University; Junseo Jung of Seoul National University; Denny Puntel of the University of Trieste; Federico Mazzola of Consiglio Nazionale delle Ricerche and Ca’ Foscari University of Venice; Shiang Fang of Google DeepMind; Chris Jozwiak, Aaron Bostwick, and Eli Rotenberg of Lawrence Berkeley National Laboratory; Jun Fuji and Ivana Vobornik of Consiglio Nazionale delle Ricerche; Jae-Hoon Park of Max Planck POSTECH/Korea Research Initiative and Pohang University of Science and Technology; Joseph G. Checkelsky, Associate Professor of Physics at MIT; and Bohm-Jung Yang of Seoul National University, who co-led the research project with Comin.
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