The DOI matches its Crossref record; 59 of the 59 references it cites were found in a registry or an index.
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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Citations
Cites
Generalized Gradient Approximation Made Simple
Perdew, J. P., Burke, K., & Ernzerhof, M. (1996) · Physical Review Letters · doi:10.1103/physrevlett.77.3865 · Cited by 215,824 · cited 4×
“We perform firstprinciples calculations based on the density functional theory with the generalized gradient approximation (GGA) [52].”
MethodInfluentialEfficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
Kresse, G., & Furthmüller, J. (1996) · Physical Review B · doi:10.1103/physrevb.54.11169 · Cited by 123,652 · cited 2×
“The electronic structure calculations are carried out using the accurate projector-augmented wave (PAW) method, as implemented in the Vienna ab-initio simulation package (VASP) [53, 54].”
MethodAb initio molecular dynamics for liquid metals
Kresse, G., & Häfner, J. (1993) · Physical review. B, Condensed matter · doi:10.1103/physrevb.47.558 · Cited by 46,097
Colloquium : Topological insulators
Hasan, M. Z., & Kane, C. L. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.3045 · Cited by 19,930
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
Thouless, D. J., Kohmoto, M., Nightingale, M. P., & den Nijs, M. (1982) · Physical Review Letters · doi:10.1103/physrevlett.49.405 · Cited by 6,973 · cited 1×
“The real projective line RP(1) ' S(1) is the only compact and connected onedimensional manifold [1].”
BackgroundBerry phase effects on electronic properties
Xiao, D., Chang, M.-C., & Niu, Q. (2010) · Reviews of Modern Physics · doi:10.1103/revmodphys.82.1959 · Cited by 5,277 · cited 2×
“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
Armitage, N. P., Mele, E. J., & Vishwanath, A. (2018) · Reviews of Modern Physics · doi:10.1103/revmodphys.90.015001 · Cited by 4,528
Self-citationObservation of a large-gap topological-insulator class with a single Dirac cone on the surface
Xia, Y., Qian, D., Hsieh, D., Wray, L., Pal, A., Lin, H., Bansil, A., Grauer, D., Hor, Y. S., Cava, R. J., et al. (2009) · Nature Physics · doi:10.1038/nphys1274 · Cited by 3,765 · cited 1×
“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.”
BackgroundMaximally localized Wannier functions: Theory and applications
Marzari, N., Mostofi, A. A., Yates, J. R., Souza, I., & Vanderbilt, D. (2012) · Reviews of Modern Physics · doi:10.1103/revmodphys.84.1419 · Cited by 3,283
Research works printed but not linked: 2
- Sturman, B. I., Fridkin, V. M. & Bradley, J. E. S. The Photovoltaic and Photorefractive Effects in Noncentrosymmetric Materials 1st edn, Vol. 8 (Routledge, 1992).
- Boyd, R. W. Nonlinear Optics 4th edn (Academic Press, 2020).
Cited by
Sorted by citations
Schlawin, F., Kennes, D. M., & Sentef, M. A. (2022) · Applied Physics Reviews · doi:10.1063/5.0083825 · Cited by 250
Essay: Where Can Quantum Geometry Lead Us?
Törmä, P. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.240001 · Cited by 187
“Moreover, work on other quantum geometric quantities, such as Christoffer symbols and Riemann curvature tensors, to describe physical phenomena has already started [15] and should be continued.”
BackgroundRecent progress in the theory of bulk photovoltaic effect
Dai, Z., & Rappe, A. M. (2023) · Chemical Physics Reviews · doi:10.1063/5.0101513 · Cited by 162
Kaplan, D., Holder, T., & Yan, B. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.026301 · Cited by 156
“linear responses carry more intricate and and the same time much more interesting information about the quantum geometry than linear response functions [53, 54].”
BackgroundGeometric deep optical sensing
Yuan, S., Ma, C., Fetaya, E., Mueller, T., Naveh, D., Zhang, F., & Xia, F. (2023) · Science · doi:10.1126/science.ade1220 · Cited by 158
“Under circularly polarized light excitation, the BPVE (injection current) is governed by the interband Berry curvature dipoles or the Hermitian metrics (54).”
Method
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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