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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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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).
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Sorted by citations
Items 101–200 of 251
Berry Curvature Spectroscopy from Bloch Oscillations
Beule, C. D., & Melé, E. J. (2023) · Physical Review Letters · doi:10.1103/physrevlett.131.196603 · Cited by 11
“Nonlinear optical responses are becoming an increasingly important tool to investigate the spectral and geometric properties of electron Bloch bands in low-dimensional materials [1–3].”
BackgroundIntrinsic nonlinear Hall effect in two-dimensional honeycomb topological antiferromagnets
Zhuang, Z.-Y., & Yan, Z. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.174443 · Cited by 10
Diagrammatic approach to excitonic effects on nonlinear optical response
Chang, Y., & Chan, Y. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.155437 · Cited by 11
“Recent theoretical study on nonlinear optical responses culminates with the establishment of its connection to quantum geometry [10–12] and topology [13].”
BackgroundQuantum transport anomalies in dispersionless quantum states
Kruchkov, A. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.l241102 · Cited by 9
Enhancing shift current response via virtual multiband transitions
Chen, S., Chaudhary, S., Refael, G., & Lewandowski, C. (2024) · Communications Physics · doi:10.1038/s42005-024-01729-z · Cited by 9
“16 ,30,31), can take advantage of this mechanism.”
BackgroundPlanar Hall plateau in magnetic Weyl semimetals
Li, L., Cui, C., Zhang, R., Yu, Z., & Yao, Y. (2024) · 中国科学通报：英文版 · doi:10.1016/j.scib.2024.11.026 · Cited by 9
Skin Effect of Nonlinear Optical Responses in Antiferromagnets
Zhou, H., Xiao, R., Zhang, S., et al. (2024) · Physical Review Letters · doi:10.1103/physrevlett.133.236903 · Cited by 9
“Typical examples are bulk photovoltaic effect (BPVE) and second harmonic generation (SHG), which involve the geometric phase of the Bloch wavefunctions and are proven to be powerful probes of symmetry and topology [2,4-7] related properties difficult to be detected using other experimental probes.”
Schüler, M., Schmitt, T., & Werner, P. (2023) · npj Quantum Materials · doi:10.1038/s41535-023-00538-x · Cited by 13
Magnetic bulk photovoltaic effect: Strong and weak field
Dai, Z., & Rappe, A. M. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.l201201 · Cited by 9
Polaron spectra and edge singularities for correlated flat bands
Pimenov, D. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.195153 · Cited by 9
“…a trivial impurity but non-trivial c -band purely as a scattering problem on Riemannian manifold which reflects the non-trival Bloch band geometry [74]; this formulation may also enable a numerically exact solution valid for all frequencies ν > 0 via bosonization and Functional Determinant…”
BackgroundZhang, J.-L., Chen, W., Liu, H.-T., Li, Y., Wang, Z., & Huang, W. (2024) · Physical Review Letters · doi:10.1103/physrevlett.132.136001 · Cited by 10
“In fact, this quantity has its origin in the quantum geometric properties of the Bloch bands [22, 23].”
BackgroundMagnetism-induced second-order nonlinear optical responses in multiferroic BiFeO 3
Prasad, B. B., Liu, G.-F., & Guo, G. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.014422 · Cited by 9
“Thus, second-order dc photocurrents can serve as a novel and effective tool for experimentally investigating the quantum geometry in materials [34, 43].”
BackgroundMethodSelf-citationElectric field induced second-order anomalous Hall transport in unconventional Rashba systems
Bhattacharya, A., & Black‐Schaffer, A. M. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.l041202 · Cited by 8
“—Recent times have witnessed a surge of interest in the quantum geometry of electrons, due to the pivotal role it has been shown to play in condensed matter [1–3, 6, 23], quantum information [14], optics [7, 8], and statistical physics [15].”
Efficient spin accumulation carried by slow relaxons in chiral tellurium
Barts, E., Tenzin, K., & Sławińska, J. (2025) · Nature Communications · doi:10.1038/s41467-025-59143-0 · Cited by 8
“This analogy makes it promising to study quantum-geometrical aspects 49,50 of spin accumulation and its lifetime in chiral materials such as Te 51 – 53 , especially in light of recently observed in ARPES experiments in-gap states 54 that aresimilar to the robust bound states localized at the chain…”
InfluentialQuantum geometry and elliptic optical dichroism in p -wave magnets
Ezawa, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/z9gw-lppc · Cited by 8
Quantum geometry and X -wave magnets with X = p, d, f, g, i
Ezawa, M. (2026) · Applied Physics Express · doi:10.35848/1882-0786/ae4311 · Cited by 9
“The injection current[6, 9, 33, 87, 88, 90– 93] and the shift current[6, 9, 33, 86–88, 90–92, 94–99] are prominent, which are second order bulk photovoltaic currents.”
InfluentialOgawa, K., Kanda, N., Murotani, Y., & Matsunaga, R. (2024) · Nature Communications · doi:10.1038/s41467-024-50186-3 · Cited by 10
“We demonstrate that the shape, orientation, rotational symmetry, and helicity of the light fi eld trajectory can be arbitrarily controlled across a broad spectral range (14 – 39THz) while maintaining phase stability.”
Regularized lattice theory for spatially dispersive nonlinear optical conductivities
Gassner, S., & Melé, E. J. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.108.085403 · Cited by 8
“[11] Junyeong Ahn, Guang-Yu Guo, Naoto Nagaosa, and Ashvin Vishwanath, “Riemannian geometry of resonant optical responses,” Nature Physics 18, 290–295 (2022).”
BackgroundLinear and non-linear response of quadratic Lindbladians
Talkington, S., & Claassen, M. (2024) · npj Quantum Materials · doi:10.1038/s41535-024-00709-4 · Cited by 8
Diverging shift current responses in the gapless limit of two-dimensional systems
Yoshida, H., & Murakami, S. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.155402 · Cited by 7
“Injection and shift currents have been attracting much attention because they are related to the quantum geometry [5, 10, 13–19].”
Extracting Nonlinear Dynamical Response Functions from Time Evolution
Ono, A. (2025) · Physical Review Letters · doi:10.1103/qsxr-c2pq · Cited by 8
Optical signatures of Euler superconductors
Chau, C. W., Jankowski, W. J., & Slager, R.-J. (2025) · Physical review. B./Physical review. B · doi:10.1103/b9ll-927t · Cited by 7
“In this regard, the notions of quantum geometry [27, 56–58] and their connections to the optical responses [27, 59, 60] are of particular interest for the superconducting states, given that quantum geometry naturally indicates the presence of nontrivial multigap invariants [27, 28], such as the…”
Quantum geometric origin of the Meissner effect and superfluid weight marker
Porlles, D., & Chen, W. (2025) · Physical review. B./Physical review. B · doi:10.1103/9fsf-9j53 · Cited by 7
Quantum Response Theory and Momentum-Space Gravity
Mehraeen, M. (2025) · Physical Review Letters · doi:10.1103/t6nt-qzws · Cited by 7
“Physically, a general viewpoint on quantum response theory that has become more prominent recently is to view it as a probe of the rich Riemannian geometry of quantum state manifolds [31].”
InfluentialQuantum geometry phenomena in condensed matter systems
Anonymous, Nagaosa, N., Ni, N., & Xu, S. (2026) · Reviews of Modern Physics · doi:10.1103/f78t-ky69 · Cited by 65
Self-citationShift photocurrent vortices from topological polarization textures
Agarwal, A., Jankowski, W. J., Bennett, D. D., & Slager, R.-J. (2025) · npj 2D Materials and Applications · doi:10.1038/s41699-025-00552-6 · Cited by 7
“The non-Abelian Berry connection defines the Hermitian connection associated with the shift photoconductivities [51], where the covariant derivative is defined with diagonal elements of the Berry connection as D a = ∂ k a − i ( A amm − A ann ).”
InfluentialNonlinear optical responses in multiorbital topological superconductors
Raj, A., Postlewaite, A., Chaudhary, S., & Fiete, G. A. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.184514 · Cited by 7
“Similar quantum geometric aspects also lead to unique signatures in light-matter coupling based processes [96] and in particular manifest very strongly in non-linear optical responses [2–4, 20, 23].”
BackgroundManipulating Photogalvanic Effects in Two-Dimensional Multiferroic Breathing Kagome Materials
Wang, H., & Yang, L. (2024) · The Journal of Physical Chemistry Letters · doi:10.1021/acs.jpclett.4c01844 · Cited by 6
Mao, D., Mendez-Valderrama, J. F., & Chowdhury, D. (2025) · Physical review. B./Physical review. B · doi:10.1103/xmz7-jgl6 · Cited by 6
Quantum geometric bounds in spinful systems with trivial band topology
Jankowski, W. J., Slager, R.-J., & Lange, G. F. (2025) · Physical Review Research · doi:10.1103/zlxq-fxgc · Cited by 6
“The calculations were performed using QuantumEspresso [16, 17], with a fully relativistic PAW pseudopotential using the PBEsol functional.”
Quantum geometric origin of the intrinsic nonlinear Hall effect
Ulrich, Y., Mitscherling, J., Classen, L., & Schnyder, A. P. (2026) · Physical review. B./Physical review. B · doi:10.1103/4z8z-4kch · Cited by 7
“To simplify the expression, we use the (hermitian) gauge-invariant interband transition rate in projector form [48, 51] such that the first derivative of the Bloch Hamiltonian yields the form ˆ P m (cid:0) ∂ a ˆ H (cid:1) ˆ P n = δ mn E an ˆ P n + i ϵ mn ˆ e .”
InfluentialWang, H., & Huang, W. (2025) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-025-2701-1 · Cited by 8
“…are closely related to the interband velocity, that is, the off-diagonal elements of the velocity operator in the band-basis representation [46, 54, 88]: V k = ( ǫ i k − ǫ j k ) h ∂ k µ ψ i k | ψ j k i , ( ǫ i k 6 = ǫ j k ), where i labels the band index, and | ψ i k i denotes the periodic…”
Photocurrents of charge and spin in monolayer Fe3GeTe2
Merte, M., Freimuth, F., Adamantopoulos, T., et al. (2021) · Physical review. B./Physical review. B · doi:10.1103/physrevb.104.l220405 · Cited by 6
Hirschmann, M. M., & Mitscherling, J. (2024) · Physical Review Materials · doi:10.1103/physrevmaterials.8.014201 · Cited by 10
Majorana Zero Modes in the Lieb-Kitaev Model with Tunable Quantum Metric
Guo, X., Ma, X., Ying, X., & Law, K. T. (2025) · Physical Review Letters · doi:10.1103/l3c7-knqm · Cited by 5
Generation of a nodal line and Weyl points by magnetization reorientation in Co3Sn2S2
Schilberth, F., Jiang, M., Mardelé, F. L., et al. (2025) · npj Quantum Materials · doi:10.1038/s41535-025-00785-0 · Cited by 5
“The quantum geometry theory for the interband optical conductivity is developedconsideringamultibandmanifoldinthereciprocalspace,leading tothede fi nition of the multiband quantum metric, also known as the quantum geometric tensor, given as the product of the Berry connections 15,16,34 .”
Self-citationHigher-order bulk photovoltaic effects, quantum geometry, and application to p -wave magnets
Ezawa, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/zt2c-v7ly · Cited by 6
“(54), where the quantum connection is defined by with[8] We generalize this relation by introducing the quantum connection to the higher-order quantum connection defined by By using it, the ℓ -th order shift conductivity is expressed in terms of it as IV. p -WAVE MAGNET In the following, we apply…”
InfluentialPalumbo, G. (2023) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad018b · Cited by 5
Zeng, X., 赖, W.-X. 文. L., Wei, Y.-W., & 马, Y.-Q. 余. M. (2023) · Chinese Physics B · doi:10.1088/1674-1056/ad1170 · Cited by 5
N-bein formalism for the parameter space of quantum geometry
Romero, J., Velasquez, C. A., & Vergara, J. D. (2024) · Journal of Physics A Mathematical and Theoretical · doi:10.1088/1751-8121/ad6f7f · Cited by 6
“[27].”
BackgroundNonlinear photomagnetization in insulators
Mendoza, B. S., Arzate, N., Tancogne-Dejean, N., et al. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.110.224412 · Cited by 5
Orbital gravitomagnetoelectric response and orbital magnetic quadrupole moment correction
Shinada, K., & Peters, R. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.214109 · Cited by 5
Nonadiabatic quantum geometry and optical conductivity
Resta, R. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.205107 · Cited by 4
“Some pioneering results in this direction appeared recently, all of them in a band-structure framework addressing the mean-field crystalline case [8–11].”
Quantization of Spin Circular Photogalvanic Effect in Altermagnetic Weyl Semimetals
Yoshida, H., Priessnitz, J., Šmejkal, L., & Murakami, S. (2026) · Physical Review Letters · doi:10.1103/463y-q7lt · Cited by 5
Quantum-Geometric Dipole: A Topological Boost to Flavor Ferromagnetism in Flat Bands
Chen, L., Ghorashi, S. A. A., Cano, J., et al. (2026) · Physical Review Letters · doi:10.1103/qbg3-3yxv · Cited by 4
“The geometric dipole of the magnon should also give rise to measurable transport phenomena, analogous to excitonic drift and shift currents [26, 27, 126], although these effects would manifest at different excitation energy scales – the energy estimates in Fig.”
Berry Curvature Dipole and Nonlinear Hall Effect in Type‐II Semi‐Dirac Systems
Liao, Z.-S., Zeng, H., Wang, E., et al. (2025) · Small · doi:10.1002/smll.202409691 · Cited by 4
Enhancing the Hyperpolarizability of Crystals with Quantum Geometry
Jankowski, W. J., Slager, R.-J., & Pizzochero, M. (2025) · Physical Review Letters · doi:10.1103/z7lp-pqp6 · Cited by 5
“We define a non-Abelian multiband quantum geometric tensor,”
Topological enhancement of nonlinear transport in unconventional point-node semimetals
Ahn, J. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.l201112 · Cited by 6
Self-citationInterstate Berry curvature of hinge state and its detection
Liu, Z., Qiao, Z., Gao, Y., & Niu, Q. (2024) · Physical Review Research · doi:10.1103/physrevresearch.6.l012005 · Cited by 4
“We comment that besides interstate Berry curvature, one can also define the interstate quantum metric tensor, which is also essential in nonlinear optical phenomena [49].”
BackgroundQuantum metric signatures in longitudinal conductivity of dispersive two-band systems
Qi, F., Cao, J., Xiang, Y., & Jin, G. (2025) · Physical review. B./Physical review. B · doi:10.1103/w9ps-c17d · Cited by 4
Reexamining circular dichroism in photoemission from a topological insulator
Sidilkover, I., Yen, Y., D'Souza, S. W., Schusser, J., Pulkkinen, A., Rotundu, C. R., Hashimoto, M., Liu, D., Shen, Z., Minár, J., et al. (2025) · Physical Review Research · doi:10.1103/g9d4-qls9 · Cited by 4
“Their far-reaching consequences include the quantum Hall effect [1], its nonlinear variant [2], light-matter coupling [3], and the identification of classes of topological materials [4] such as Weyl semimetals.”
Lou, Z., Gong, Z., Zhu, Z., Li, W., Lin, X., & Wang, H. (2025) · Physical review. B./Physical review. B · doi:10.1103/z7v3-7ct4 · Cited by 3
Field-Driven Band Asymmetry and Nonreciprocal Transport in a Helimagnet
Deaconu, D., Agarwal, A., Belosludov, R. V., et al. (2025) · Physical Review Letters · doi:10.1103/lhj4-9h29 · Cited by 3
Universal intrinsic orbital dynamics from Berry curvature in electronic two-band systems
Lee, J. M. (2025) · Physical review. B./Physical review. B · doi:10.1103/42mj-sh8x · Cited by 6
“Nonlinear responses may reveal additional geometric contributions beyond the Berry curvature, such as the quantum metric [2, 87].”
Phonon spectra, quantum geometry, and the Goldstone theorem
Pellitteri, G., Dai, Z., Hu, H., Jiang, Y., Menichetti, G., Tomadin, A., Bernevig, B. A., & Polini, M. (2025) · Physical review. B./Physical review. B · doi:10.1103/jg8x-l6h6 · Cited by 4
“Quantum transport anomalies in systems with flat bands [51] as well as non-linear optical response functions [52] have also been linked to the quantum geometry of states.”
From quantum geometry to nonlinear optics and gerbes: Recent advances in topological band theory
Bzdušek, T. (2026) · Physical review. B./Physical review. B · doi:10.1103/9p92-qt26 · Cited by 8
“…) , with a, b ∈ { x, y, z } ] can be related using the Kubo-Greenwood formula to an integral involving the inter-band Berry connection (also called optical dipole ) A nma = ⟨ u n | ∂ a u m ⟩ , which encodes geometrical information about the optical transitions between the energy bands n and m [12].”
Light-induced nonlinear spin Hall current in single-layer WTe2
Bhalla, P., & Rostami, H. (2024) · New Journal of Physics · doi:10.1088/1367-2630/ad2822 · Cited by 3
“There is, however, a growing interest in the third-order rectified current that can be achieved in the presence of an extra direct electric field j (3) dc ∼ E dc E ( ω ) E ∗ ( ω ) which can induce rectified current in centrosymmetric systems [52–54].”
BackgroundGeometric semimetals and their simulation in synthetic matter
Lin, Y., & Palumbo, G. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.l201107 · Cited by 3
Quantum Geometry and Bounds on Dissipation in Slowly Driven Quantum Systems
Esin, I., Lantagne-Hurtubise, É., Nathan, F., & Refael, G. (2025) · Physical Review Letters · doi:10.1103/physrevlett.134.146603 · Cited by 3
Nonlinear Hall effect driven by spin-charge-coupled motive force
Hattori, K., Watanabe, H., & Arita, R. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.174416 · Cited by 4
“When X = Y = E , the generalized quantum metric and Berry curvature are the conventional quantum metric and Berry curvature, respectively [67].”
Bicircular light-induced multistate geometric current
Guo, Z., Lu, Z., Wang, H., & Chang, K. (2025) · Physical review. B./Physical review. B · doi:10.1103/7ytw-vyb7 · Cited by 3
Quantum Geometry in Phonon-Mediated Optical Responses
Hu, J., Li, W., Guo, Z., Wang, H., & Chang, K. (2025) · Physical Review Letters · doi:10.1103/y66p-kjj7 · Cited by 9
Ünal, F. N., Nardin, A., & Goldman, N. (2025) · Physical Review Letters · doi:10.1103/6d6n-3trh · Cited by 9
Optically induced umklapp shift currents in striped cuprates
Dolgirev, P. E., Michael, M. H., Curtis, J. B., et al. (2024) · Physical review. B./Physical review. B · doi:10.1103/physrevb.109.045150 · Cited by 3
Sun, Z., Wang, T., Jin, H., et al. (2025) · Advanced Science · doi:10.1002/advs.202505860 · Cited by 3
Superconducting Berry Curvature Dipole
Matsyshyn, O., Vignale, G., & Song, J. C. W. (2026) · Physical Review Letters · doi:10.1103/gbcm-l2qd · Cited by 2
“…electrons with a range of nonreciprocal responses that include nonlinear Hall currents even in the presence of time-reversal symmetry [2, 8, 9], electro-optic modulation and amplification without population inversion [10–12], as well as means for energy harvesting in the terahertz regime [11].”
Shift spin photocurrents in two-dimensional systems
Hsu, H.-C., & Chen, T.-W. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.115413 · Cited by 2
“Recent studies have demonstrated that the bulk photovoltaic effect is cosely related to the geometrical properties of Bloch states [6–8], stretching the fundamental understanding of materials beyond energy bands [9].”
Fujimoto, T., Murotani, Y., Tamaya, T., Kurihara, T., Kanda, N., Kim, C., Yoshinobu, J., Akiyama, H., Kato, T., & Matsunaga, R. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.l201201 · Cited by 2
Phonon-mediated shift currents in twisted bilayer MoS2
Huang, B., Li, S., Li, B., et al. (2025) · Applied Physics Letters · doi:10.1063/5.0288528 · Cited by 2
Multi‐Parameter Infrared Photodetection Based on Topological Semimetals
Niu, P., Liu, H., Zhang, P., & Lai, J. (2025) · Advanced Optical Materials · doi:10.1002/adom.202502083 · Cited by 2
Diamagnetic Meissner response of odd-frequency superconducting pairing from quantum geometry
Bhattacharya, A., & Black‐Schaffer, A. M. (2026) · Physical review. B./Physical review. B · doi:10.1103/c57s-skv9 · Cited by 2
“The real part of the QGT, known as the quantum metric, is crucial in various higher-order transport processes [14–16], resonant optical responses [17,18], and fractional Chern insulators [19,20], along with generating a finite superfluid weight in flat-band superconductors [3–6].”
Geometric Bloch oscillations and transverse displacement in flat band systems
Liu, J. M., Palumbo, G., & Liberto, M. F. D. (2025) · Physical review. B./Physical review. B · doi:10.1103/3fdj-mttf · Cited by 4
Quantum geometric tensors from sub-bundle geometry
Oancea, M. A., Mieling, T., & Palumbo, G. (2026) · Quantum · doi:10.22331/q-2026-01-14-1965 · Cited by 4
“Note that this differential-geometric version of torsion is different from the one already used in condensed matter physics [147, 148], where a notion of torsion arises in quantum systems with more than two subspaces.”
Geodesic Nature and Quantization of Shift Vector
Wang, H., & 常, K. 凯. C. (2025) · Chinese Physics Letters · doi:10.1088/0256-307x/43/2/020703 · Cited by 3
Quantum geometry of common semiconductors
Porlles, D., & Chen, W. (2026) · Applied Physics Letters · doi:10.1063/5.0307679 · Cited by 2
“…this metric enters the optical transition matrix elements of interband transitions 4 , it manifests in many optical responses like optical conductivity 5 , capacitance 6 , dielectric function, charge susceptibility, refractive index, absorption coefficient, reflectance, and transmittance 7 .”
Nonadiabatic wave-packet dynamics: Nonadiabatic metric, quantum geometry, and gravitational analogy
Ren, Y., & Barrero, M. E. S. (2026) · Physical review. B./Physical review. B · doi:10.1103/pwvz-868b · Cited by 5
Mass-invariant universal optical conductivity from quantum geometry
Oh, C., Kim, S.-W., Kim, K. W., Monserrat, B., & Rhim, J. (2026) · Science Advances · doi:10.1126/sciadv.ady2033 · Cited by 2
“Moreover, it modifies the quantum metric, thereby influencing the optical response, including both linear and higher-order nonlinear optical conductivities ( 37 , 41 – 43 ).”
Thermal Uhlmann phase in a locally driven two-spin system
Villavicencio, J., Cota, E., Rojas, F., Maytorena, J. A., Galindo, D. M., & Nieto-Guadarrama, F. (2023) · Physical Review A · doi:10.1103/physreva.107.062222 · Cited by 2
Song, B. Q., Smith, J. D. H., Jiang, T., et al. (2025) · Physical review. B./Physical review. B · doi:10.1103/physrevb.111.144305 · Cited by 2
Circular photon drag effect in Dirac electrons by quantum geometry
Qu, G. (2025) · Physical review. B./Physical review. B · doi:10.1103/dk8k-zm7b · Cited by 2
“…the quantum geometric tensor [6]: Here, A βc,σ ; v,τ is the interband Berry connection outside the degenerate subspace, which equals to interband matrix element of position operator [37] and serves as a tangent basis vector for constructing complex Riemannian structure of optical transitions [2].”
InfluentialQuantum Geometric Origin of Strain-Induced Ferroelectric Phase Transitions
Hu, J., Zhu, Z., Yuan, Y., Wang, H., & Chang, K. (2025) · Physical Review Letters · doi:10.1103/dbxd-jk76 · Cited by 2
“The geometric properties of quantum states are increasingly recognized as critical for understanding various condensed-matter phenomena [24–37].”
Quantum geometry induced second harmonic generationPreprint
Bhalla, P., Das, K., Culcer, D., & Agarwal, A. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2108.04082 · Cited by 2
“The quantum geometric connection is decomposed into real and imaginary parts C mp = Γ mp−iΓ̃ mp, where Γ (Γ̃) is the metric (symplectic) connection [33].”
BackgroundElectrons flow like falling cats: Deformations and emergent gravity in quantum transportPreprint
Holder, T. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2111.07782 · Cited by 2
“Here we mention in particular the recent observation that the third order electrical conductivity [34,35] - a four index object - can be expressed with the help of a Riemann curvature tensor [36].”
BackgroundSingular-connection approach to topological phases and resonant optical responses
Mera, B., & Ozawa, T. (2022) · Physical review. B./Physical review. B · doi:10.1103/physrevb.106.245134 · Cited by 1
“[15], a topological invariant for the optical transition between two bands is introduced, which is the difference of the Chern numbers of the two bands.”
BackgroundInfluentialSong, B. Q., Smith, J. D. H., & Wang, J. (2026) · Quantum Reports · doi:10.3390/quantum8010014 · Cited by 4
Circular-polarization-selective perfect reflection from chiral superconductors
Ahn, J., & Vishwanath, A. (2025) · Nature Communications · doi:10.1038/s41467-025-61658-5 · Cited by 1
“To put our work in a broader scope, let us note that the role of topology 24 – 27 and, more broadly, geometry 28 – 32 of quantum states in functional optical properties of materials has been intensively studied recently.”
Self-citationPure spin and orbital bulk photovoltaic effect in topological screw dislocations
Yang, M., Zhang, C., & Zhou, J. (2025) · Physical review. B./Physical review. B · doi:10.1103/y3bz-fh8v · Cited by 1
Guan, Y., & Bradlyn, B. (2026) · Physical Review Research · doi:10.1103/3xjs-c7v7 · Cited by 1
“…in the quasistatic limit to find (104) We now apply these results to study the quasistatic Bures connection in the case of noninteracting crystalline systems at zero temperature, where there has been much interest in quantum geometric contributions to nonlinear conductivities [17, 18, 22, 26, 83].”
InfluentialWang, X., He, X., & Wu, J. (2025) · Physical review. B./Physical review. B · doi:10.1103/rw2m-33v6 · Cited by 2
Quantum geometric map of magnetotransport
Xiang, L., Jia, J., Xu, F., et al. (2026) · Physical review. B./Physical review. B · doi:10.1103/kd12-4ycj · Cited by 1
Band geometry induced third-harmonic generation
Sarkar, S., Mandal, D., & Agarwal, A. (2025) · Physical review. B./Physical review. B · doi:10.1103/537j-v1lp · Cited by 1
“Our analysis shows that THG is governed by five key quantum geometric quantities: quantum metric ( G abnm ), Berry curvature (Ω abnm ), metric connection (Γ abcnm ), symplectic connection (˜Γ abcnm ), and the second-order connection ( D abcdnm ) [40].”
Nonlinear Optical Effects Enhanced by Deep Band Crossings
Zou, N., Li, H., Ye, M., Chen, H., Sun, M., Guo, R., Liu, Y., Gu, B., Duan, W., Xu, Y., et al. (2025) · Physical Review Letters · doi:10.1103/sqwy-xhdf · Cited by 2
Isoperimetric Inequalities in Quantum Geometry
Pai, P., & Zhang, F. (2026) · Physical Review Letters · doi:10.1103/h9vk-lrvk · Cited by 1
“Examples are abundant: various Hall effects [2–5], flat-band superconductivity [8, 9], orbital magnetism [10], resonant optical responses [11], and not to mention topological phases of matter [12].”
Giant shift current in electrically tunable superlattice bilayer graphene
Atlam, N., Chaudhary, S., Raj, A., et al. (2025) · Physical review. B./Physical review. B · doi:10.1103/3npr-fqt1 · Cited by 1
“[25], Eq.”
Yang, B. (2026) · Chinese Physics Letters · doi:10.1088/0256-307x/43/2/020712 · Cited by 1
Bulk photovoltaic effects in mirror-time symmetric systems
Lin, B.-X., & Hsu, H.-C. (2026) · Physical review. B./Physical review. B · doi:10.1103/xqyz-wtc7 · Cited by 1
Takagi, T., Watanabe, H., Yoshimi, R., Sato, Y., Toyoda, S., Tsukazaki, A., Takahashi, K., Kawasaki, M., Tokura, Y., & Ogawa, N. (2026) · Physical review. B./Physical review. B · doi:10.1103/dp31-y358 · Cited by 2
Quantum Geometric Inequality and Its Classical Wave Verification
Zhang, Q., Zhang, Q., & Qiu, C. (2026) · Physical Review Letters · doi:10.1103/8312-ntt5 · Cited by 1
Liao, Z.-S., Xu, Z., Wang, E., et al. (2026) · Physical review. B./Physical review. B · doi:10.1103/9wgk-g3dd · Cited by 1
Nonadiabatic origin of quantum-metric effects via momentum-space metric tensor
Ren, Y. (2026) · Physical review. B./Physical review. B · doi:10.1103/k7yb-5c9t · Cited by 1
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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