Riemannian geometry of resonant optical responses
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The nonlinear optical response of topological materials can be framed in terms of local geometric quantities originating from interband Berry connection.
“While it is possible to frame the nonlinear optical response of topological materials in terms of local geometric quantities originating from interband Berry connection44,95”
From Ultrafast terahertz emission from emerging symmetry-broken materials (2023) · cites this paper as [95]
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“51 The KBSS formula has been derived in a variety of models and methods,[4, 6, 7, 12, 13, 15, 16, 18, 19, 85] which may have created an impression that the KBSS formula is universally truthful.”
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“Recent studies by the present authors [27, 28] allow a stronger quantum geometric interpretation that the interband superfluid weight is quantum geometric even away from the flat-band limit.”
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“The modern quantum geometric perspective on D ( k ) establishes a link between dipole transitions and the Berry connection 72 , thus to topological properties.”
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“The injection current is related to Berry curvature [5, 12] and quantum metric [6, 7], while the shift current is related to Hermitian connections [1, 9, 24].”
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“…state tomography of cold atoms [29], and transmission measurements of plasmonic lattices [30], as well as theoretical works on optical response [31], quantum fluctuations of the QGT [32], quantum phase transitions [33], superfluidity in flat bands [34], generalizations to N -band systems [35],…”
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Magnetic bulk photovoltaic effect as a probe of magnetic structures of $\mathrm{{EuSn_{2}As_{2}}}$
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“These mechanisms for a BPVE are intimately related to the quantum geometry of the electronic wavefunction [14, 15], and thus are proving to be reliable tools to probe and utilize the band topology [6, 7].”
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Quantum geometry and nonlinear optical responses in rhombohedral trilayer graphene
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“Third-order responses were also studied and correlated with the Riemannian curvature tensor [60], and the superconducting quasi-particle Berry curvature was found to play a key role in the nonlinear optical response of a noncentrosymmetric superconductor [68].”
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Spin Transport Revealed by Spin Quantum Geometry
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Nonlinear Hall Effect from Long-Lived Valley-Polarizing Relaxons
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“By combining the relaxon analysis and the theories of nonlinear transport including band-geometric effects [7, 9, 57–59] using ab initio scattering matrices [60, 61], one can reveal novel response properties of real materials beyond the RTA, as demonstrated in this work for the NLH effect.”
MethodAnomalous geometric transport signatures of topological Euler class
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Quantum geometric bounds for observables: Linear responses, Drude weight, and orbital magnetization
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“Furthermore, the extension to higher-order geometric quantities such as connection and its relation with nonlinear responses have recently been discussed [34–37].”
Self-citation
- Authors
- Ahn, J., Guo, G.-Y., Nagaosa, N., & Vishwanath, A.
- Affiliations
- Harvard University (US)
- National Taiwan University (TW)
- RIKEN (JP)
- Venue
- Nature Physics
- Published
- 2021-12-23
- Volume
- 18
- Issue
- 3
- Pages
- 290-295
- ISSN
- 1745-2473 (ISSN-L)
- 1745-2481
- OpenAlex
- W3134879942
- Cited by
- 252
- References
- 54
- Citations by year
- 2026: 58 · 2025: 75 · 2024: 55 · 2023: 35 · 2022: 21 · 2021: 8
- FWCI
- 12.99
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Licence
- Locations
- Nature Physics (publishedVersion)
- arXiv (Cornell University) (acceptedVersion)
- Digital Access to Scholarship at Harvard (DASH) (Harvard University) (acceptedVersion)
- Figshare (submittedVersion, cc-by)
- arXiv (Cornell University) (cc-by)
- Funders
- DOE | LDRD | Ames Laboratory (DE-AC02-07CH11358)
- National Research Foundation of Korea (2020R1A6A3A03037129)
- Ministry of Science and Technology, Taiwan
- MEXT | Japan Science and Technology Agency (JPMJCR1874, JPMJCR16F1)
- MEXT | Japan Society for the Promotion of Science (18H03676)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Quantum and electron transport phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › Advanced Condensed Matter Physics
- Keywords
- Riemannian geometry, quantum geometry, transition dipole moment, Riemann curvature tensor, Berry phase, quantum Hall effect, anomalous Hall effect, optical transitions
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