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Direct measurement of the quantum metric tensor in solids.

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Title: Direct measurement of the quantum metric tensor in solids.
Authors: Kim, Sunje, Chung, Yoonah, Qian, Yuting, Park, Soobin, Jozwiak, Chris, Rotenberg, Eli, Bostwick, Aaron, Kim, Keun Su, Yang, Bohm-Jung
Source: Science. 6/5/2025, Vol. 388 Issue 6751, p1050-1054. 5p.
Subjects: Quantum states, Momentum space, Photoelectron spectroscopy, Photoemission, Optical polarization
Abstract: 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. In this work, we report a direct measurement of the full quantum metric tensors of Bloch electrons in solids using black phosphorus as a representative material. We extracted 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. Editor's summary: The quantum metric, the real part of the complex-valued quantum geometric tensor, has a bearing on the electronic properties of solids, including transport. Although the quantum metric has been measured directly in artificial systems, determining the full tensor in solids has proven tricky. Kim et al. extracted this quantity using photoemission measurements in black phosphorus. The researchers expect that their methodology can be extended to other materials with related band structures. —Jelena Stajic [ABSTRACT FROM AUTHOR]
Copyright of Science is the property of American Association for the Advancement of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Psychology and Behavioral Sciences Collection
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  Data: Direct measurement of the quantum metric tensor in solids.
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  Data: <searchLink fieldCode="AR" term="%22Kim%2C+Sunje%22">Kim, Sunje</searchLink><br /><searchLink fieldCode="AR" term="%22Chung%2C+Yoonah%22">Chung, Yoonah</searchLink><br /><searchLink fieldCode="AR" term="%22Qian%2C+Yuting%22">Qian, Yuting</searchLink><br /><searchLink fieldCode="AR" term="%22Park%2C+Soobin%22">Park, Soobin</searchLink><br /><searchLink fieldCode="AR" term="%22Jozwiak%2C+Chris%22">Jozwiak, Chris</searchLink><br /><searchLink fieldCode="AR" term="%22Rotenberg%2C+Eli%22">Rotenberg, Eli</searchLink><br /><searchLink fieldCode="AR" term="%22Bostwick%2C+Aaron%22">Bostwick, Aaron</searchLink><br /><searchLink fieldCode="AR" term="%22Kim%2C+Keun+Su%22">Kim, Keun Su</searchLink><br /><searchLink fieldCode="AR" term="%22Yang%2C+Bohm-Jung%22">Yang, Bohm-Jung</searchLink>
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  Data: <searchLink fieldCode="DE" term="%22Quantum+states%22">Quantum states</searchLink><br /><searchLink fieldCode="DE" term="%22Momentum+space%22">Momentum space</searchLink><br /><searchLink fieldCode="DE" term="%22Photoelectron+spectroscopy%22">Photoelectron spectroscopy</searchLink><br /><searchLink fieldCode="DE" term="%22Photoemission%22">Photoemission</searchLink><br /><searchLink fieldCode="DE" term="%22Optical+polarization%22">Optical polarization</searchLink>
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  Data: 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. In this work, we report a direct measurement of the full quantum metric tensors of Bloch electrons in solids using black phosphorus as a representative material. We extracted 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. Editor's summary: The quantum metric, the real part of the complex-valued quantum geometric tensor, has a bearing on the electronic properties of solids, including transport. Although the quantum metric has been measured directly in artificial systems, determining the full tensor in solids has proven tricky. Kim et al. extracted this quantity using photoemission measurements in black phosphorus. The researchers expect that their methodology can be extended to other materials with related band structures. —Jelena Stajic [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Science is the property of American Association for the Advancement of Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1126/science.ado6049
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        Text: English
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      – SubjectFull: Photoelectron spectroscopy
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      – SubjectFull: Photoemission
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      – SubjectFull: Optical polarization
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              Text: 6/5/2025
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