December 18, 2024 by Ingrid Fadelli , Phys.org

Collected at: https://phys.org/news/2024-12-approach-possibilities-quantum-geometry-solids.html

Understanding and reliably measuring the geometric properties of quantum states can shed new light on the intricate underpinning of various physical phenomena. The quantum geometric tensor (QGT) is a mathematical object that provides a detailed description of how quantum states change in response to perturbations, thus offering insights about their underlying geometry.

While this mathematical object has been the focus of numerous theoretical studies, measuring it in experimental settings has proved more challenging. As a result, direct measurements of the QGT have so far been limited to artificial two-level systems.

Researchers at Massachusetts Institute of Technology, Seoul National University and other institutions recently devised a new approach to measure the QGT in crystalline solids. Their proposed method, introduced in a Nature Physics paper, relies on photoemission spectroscopy, a technique typically used to examine the electronic structure of materials.

“The work started as we were thinking about ways to probe the Berry curvature of electrons in solids,” Riccardo Comin, senior author of the paper, told Phys.org. “We originally devised an experiment based on the relationship between orbital angular momentum (probed by circular dichroic ARPES) and Berry curvature.”

The first experiment carried out by Comin and his colleagues was successful and it allowed them to compile the dataset that they used to conduct their recent study. This ultimately allowed them to develop their new approach for measuring QGT in solids, which they called “reconstruction of the full QGT.”

“The full scope of our method was developed thanks to work in Prof. Yang’s group, where the approach was broadened to include the reconstruction of the real part of the quantum geometric tensor (the quantum distance) from the energy dispersion of electronic bands,” said Comin.

“From there, we were able together to develop an approach that connects band theory with experimental data from ARPES, which is the key advancement of this paper.”

A method to measure the quantum geometric tensor in solids
Credit: Kang et al.

The approach devised by Comin, Prof. Yang and their colleagues is based on two independent but complementary approaches. Both of these approaches entail the analysis of data collected via angle-resolved photoemission spectroscopy (ARPES), as a means of retrieving both the real (i.e., quantum distance) and imaginary (i.e., Berry curvature) parts of the QGT.

“The method requires the use of spin- and polarization-resolved ARPES and relies on a minor set of approximations, which are outlined in the paper,” explained Comin.

“Notably, the method was conceived to be applicable to any generic material, regardless of its band structure details or symmetry properties. What makes our approach more powerful is that the QGT is resolved for each electron in reciprocal space.

“This is a significant step forward from existing methods which can mainly detect an integrated Berry curvature (a.k.a., the Chern number) via linear or nonlinear transport measurements.”

The recent study by Comin, Prof. Yang and their colleagues opens new possibilities for research focusing on the geometric properties of quantum states in solids. The new approach they developed could soon be used to study various crystalline systems, which could enrich the current understanding of their quantum geometric responses.

“The most important implication is that we now have a way to retrieve information about the electron wavefunction, and not just the electron energy levels (i.e., the electronic bands),” added Comin.

“This will make it possible to establish an even closer connection between experiments and theory. In our next studies, we plan to apply this method to a broad class of materials with nontrivial topology, to elucidate the detailed origin of quantum geometrical effects.”

More information: Mingu Kang et al, Measurements of the quantum geometric tensor in solids, Nature Physics (2024). DOI: 10.1038/s41567-024-02678-8.

Journal information: Nature Physics 

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