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

 

Authors: Mingu Kang*, Sunje Kim*, Yuting Qian, Paul M. Neves, Linda Ye, Junseo Jung, Denny Puntel, Federico Mazzola, Shiang Fang, Chris Jozwiak, Aaron Bostwick, Eli Rotenberg, Jun Fuji, Ivana Vobornik, Jae-Hoon Park, Joseph G. Checkelsky, Bohm-Jung Yang† & Riccardo Comin†

(*: First author, †: Corresponding author)

 

Publication date: 25 November 2024

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