The quantum metric tensor is a central geometric quantity in modern physics that is defined as the distance between nearby quantum states. Despite numerous studies highlighting its relevance to fundamental physical phenomena in solids, measuring the complete quantum metric tensors in real solid-state materials is challenging. Here, we report a direct measurement of the full quantum metric tensors of Bloch electrons in solids using black phosphorus as a representative material. We extract the momentum space distribution of the pseudospin texture of the valence band from the polarization dependence of angle-resolved photoemission spectroscopy measurement. Our approach is poised to advance our understanding of quantum geometric responses in a wide class of crystalline systems.

 

Authors: Sunje Kim†, Yoonah Chung†, Yuting Qian†, Soobin Park, Chris Jozwiak, Eli Rotenberg, Aaron Bostwick, Keun Su Kim* & Bohm-Jung Yang*

 

Publication date: 5 June 2025

Link: Science 388, 1050-1054 (2025) – Direct measurement of the quantum metric tensor in solids (science.org)