Physicists measure quantum geometry for first time

Alright, this one is pretty interesting but, as usual, it needs some amount of background to appreciate it properly. Let me try to make an elementary summary.

Electrons in a crystal are partially governed by a "quantum metric" on the "Brillouin zone manifold" [1]. Metric tensors on manifolds famously appear in general relativity, and are a central object in differential geometry (hence the accurate moniker "quantum geometry"). "Quantum geometry" is a hot topic in condensed matter physics in the last few years, and governs or is connected to many important quantities. For instance, the integral of the quantum metric is proportional to the conductivity (in the disorder-free regime) [2]. This paper makes a more-or-less direct measurement of the quantum metric in the material CoSn.

[1] https://doi.org/10.1007/BF02193559 [2] https://doi.org/10.1103/PhysRev.133.A171, https://doi.org/10.1103/PhysRevB.62.1666

The paper itself:

https://www.nature.com/articles/s41567-024-02678-8

Why not link to the papers themselves on HN? They usually are not hard to read, at least the abstract, introduction, etc. And the papers provide excellent background, references, etc. For example,

Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.

Some interesting commentary from the lead researcher:

Kang stresses that the new ability to measure the quantum geometry of materials "comes from the close cooperation between theorists and experimentalists."

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.

As usual, journalists write clickbait titles. The quantum geometric tensor has not been measured for the first time. Perhaps it’s a novel way to measure it in a crystal, but certainly it’s a very well known concept in quantum physics. I’ve worked with it too to perform natural gradient descent on the space of quantum states.

Is "quantum geometry" a common way to say "shape of the wave function" in solid-state physics?

Here I was, thinking the article would be about a topic at the intersection of quantum mechanics and relativity…