Researchers at the Massachusetts Institute of Technology, Seoul National University, and other institutions have made a crucial advancement in understanding the geometric properties of quantum states. The team, led by Riccardo Comin and Bohm-Jung Yang, has developed a framework to measure the Quantum Geometric Tensor in crystalline solids using polarization-, spin-, and angle-resolved photoemission spectroscopy. This breakthrough advances our understanding of quantum geometric responses in various materials.
The quantum geometric tensor (QGT) is a fundamental concept that encapsulates the geometric characteristics of quantum states. It plays a pivotal role in explaining various physical phenomena, particularly those involving topological and quantized effects. The QGT comprises two essential components: the quantum metric, representing the real part, and the Berry curvature, which constitutes the imaginary part. These elements provide insights into the intrinsic geometry of quantum systems.
Companies such as the Advanced Light Source at Lawrence Berkeley National Laboratory and institutions like the Max Planck POSTECH/Korea Research Initiative have contributed to this work. The team’s findings have significant implications for the study of topological materials and could lead to new technologies and applications in fields such as quantum computing and materials science.
The Berry curvature is a theoretical magnetic field in parameter space, underpinning the mechanisms behind topological and quantized phenomena. Meanwhile, the quantum metric quantifies the separation between quantum states in parameter space, correlating with quantum fluctuations, dissipative properties, and fidelity susceptibility. Together, they form the foundational framework for analyzing geometric and topological properties in quantum materials.
Despite its theoretical importance, the practical measurement of the QGT has largely been confined to simplified two-level systems, such as superconducting qubits and nitrogen-vacancy centers in diamonds. Conducting direct measurements of the QGT within solid materials, where electron energy and momentum vary, has posed a significant experimental challenge, limiting the exploration of QGT in more complex environments.
The authors introduce the quasi-QGT, a novel tensor approximating the QGT to address this. The quasi-QGT’s real component corresponds to the band Drude weight (BDW), while its imaginary component reflects the orbital angular momentum (OAM). This quasi-QGT accurately mirrors the QGT in two-band systems and provides a reliable approximation in systems with multiple bands, broadening its applicability across various material platforms.
The authors experimentally validate this framework through photoemission spectroscopy in the kagome metal CoSn, known for its topological flat bands. This approach enables the reconstruction of the quantum metric and spin Berry curvature, offering observable evidence of topological flat bands. Such measurements mark a significant step forward in direct experimental access to QGT properties in crystalline solids.
Beyond kagome metals, the authors suggest extending this method to other two-dimensional materials, including hexagonal boron nitrides and monolayer black phosphorus. By facilitating QGT measurement in diverse materials, this new methodology offers a transformative tool for advancing the study of quantum geometric responses, potentially reshaping the understanding of electronic properties in quantum materials.
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