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Riemannian geometry of resonant optical responses
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“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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Cites
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“As we show in Supplementary Note 3, w 1 = w n 1 − w 1 , (63) where w 1 and w m 1 are the first Stiefel-Whitney numbers of bands n and m, or equivalently, the Berry phases of bands n and m divided by π [3, 4].”
BackgroundNagaosa, N., Sinova, J., Onoda, S., MacDonald, A. H., & Ong, N. P. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1539 · Cited by 4,798
Self-citationWeyl and Dirac semimetals in three-dimensional solids
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“These materials are Z2 topological insulators in two and three dimensions [37, 38], and a Chern insulator [39], respectively, described by a massive Dirac Hamiltonian close to the band edge.”
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“…QGT has recently been shown to play a key role in many seemingly disparate areas of condensed matter, ranging from flat-band superconductivity [14–16], capacitance in insulators [17–19], the fractional quantum anomalous Hall effect [20–23], and, the focus of this work, optical responses [24–33].”
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“Future work may explore the application of this Fourier expansion to many-body systems, the detection of topological transitions in higher-dimensional parameter spaces, establish the relation between classical and quantum chaos, and resonant optical responses [ 60 ].”
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“A paradigmatic example is the bulk photovoltaic effect [41–46], in which a dc photocurrent is generated as a second-order response to the electric field, and the corresponding non-linear conductivity can be expressed in terms of geometric quantities [47–51].”
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Metadata
- 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 › Condensed Matter Physics › Topological Materials and Phenomena
- Physical Sciences › Physics and Astronomy › Condensed Matter Physics › 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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