Polman, A., Knight, M., Garnett, E. C., Ehrler, B. & Sinke, W. C. Photovoltaic materials: present efficiencies and future challenges. Science 352, aad4424 (2016).
Sturman, B. I & Fridkin, V. M. Photovoltaic and Photo-Refractive Effects in Noncentrosymmetric Materials (Gordon and Breach Science Publisher, 1992).
Morimoto, T. & Nagaosa, N. Topological nature of nonlinear optical effects in solids. Sci. Adv. 2, e1501524 (2016).
Morimoto, T. & Nagaosa, N. Topological aspects of nonlinear excitonic processes in noncentrosymmetric crystals. Phys. Rev. B 94, 035117 (2016).
Ma, Q., Grushin, A. G. & Burch, K. S. Topology and geometry under the nonlinear electromagentic spotlight. Nat. Mater. 20, 1601–1614 (2021).
Ma, Q., Kumar, R. K., Xu, S., Koppens, F. H. L. & Song, J. C. W. Photocurrent as a multiphysics diagnostic of quantum materials. Nat. Rev. Phys. 5, 170–184 (2023).
Grinberg, I. et al. Perovskite oxides for visible-light-absorbing ferroelectric and photovoltaic materials. Nature 503, 509–512 (2013).
Ogawa, N., Sotome, M., Kaneko, Y., Ogino, M. & Tokura, Y. Shift current in the ferroelectric semiconductor SbSI. Phys. Rev. B 96, 241203 (2017).
Ma, Q. et al. Direct optical detection of Weyl fermion chiralty in a topological semimetal. Nat. Phys. 13, 842–847 (2017).
Osterhoudt, G. B. et al. Colossal mid-infrared bulk photovoltaic effect in a type-I Weyl semimetal. Nat. Mater. 18, 471–475 (2019).
Xu, S. et al. Electrically switchable Berry curvature dipole in the monolayer topological insulator WTe2. Nat. Phys. 14, 900–906 (2018).
Zhang, Y. et al. Enhanced intrinsic photovoltaic effect in tungsten disulfide nanotubes. Nature 570, 349–353 (2019).
Akamatsu, T. et al. A van der Waals interface that creates in-plane polarization and a spontaneous photovoltaic effect. Science 372, 68–72 (2021).
Zhang, Y. et al. Switchable magnetic bulk photovoltaic effect in the two-dimensional magnet CrI3. Nat. Commun. 10, 3783 (2019).
Xu, H., Wang, H., Zhou, J. & Li, J. Pure spin photocurrent in non-centrosymmetric crystals: bulk spin photovoltaic effect. Nat. Commun. 12, 4330 (2021).
Wang, H. & Qian, X. Electrically and magnetically switchable nonlinear photocurrent in PT-symmetric magnetic topological quantum materials. NPJ Comput. Mater. 6, 199 (2020).
Fei, R., Song, W., Pusey-Nazzaro, L. & Yang, L. PT-symmetry-enabled spin circular photogalvanic effect in antiferromagnetic insulators. Phys. Rev. Lett. 127, 207402 (2021).
Ahn, J., Guo, G. & Nagaosa, N. Low-frequency divergence and quantum geometry of the bulk photovoltaic effect in topological semimetals. Phys. Rev. X 10, 041041 (2020).
Watanabe, H. & Yanase, Y. Chiral photocurrent in parity-violating magnet and enhanced response in topological antiferromagnet. Phys. Rev. X 11, 011001 (2021).
Holder, T., Kaplan, D. & Yan, B. Consequences of time-reversal-symmetry breaking in the light-matter interaction: Berry curvature, quantum metric, and diabatic motion. Phys. Rev. Res. 2, 033100 (2020).
Jiang, Y., Holder, T. & Yan, B. Revealing quantum geometry in nonlinear quantum materials. Rep. Prog. Phys. 88, 076502 (2025).
Dai, Z. & Rappe, A. M. Recent progress in the theory of bulk photovoltaic effect. Chem. Phys. Rev. 4, 011303 (2023).
Ogawa, N., Bahramy, M. S., Murakawa, H., Kaneko, Y. & Tokura, Y. Magnetophotocurrent in BiTeI with Rashba spin-split bands. Phys. Rev. B 88, 035130 (2013).
Ogawa, N. et al. Zero-bias photocurrent in ferromagnetic topological insulator. Nat. Commun. 7, 12246 (2016).
Matsubara, M. et al. Polarization-controlled tunable directional spin-driven photocurrents in a magnetic metamaterial with threefold rotational symmetry. Nat. Commun. 13, 6708 (2022).
Song, T. et al. Spin photovoltaic effect in magnetic van der Waals heterostructures. Sci. Adv. 7, eabg8094 (2021).
Huang, B. et al. Layer-dependent ferromagnetism in a van der Waals crystal down to the monolayer limit. Nature 546, 270–273 (2017).
Gong, C. et al. Discovery of intrinsic ferromagnetism in two-dimensional van der Waals crystals. Nature 546, 265–269 (2017).
Wang, Z. et al. Magnetization dependent tunneling conductance of ferromagnetic barriers. Nat. Commun. 12, 6659 (2021).
Cai, X. et al. Atomically thin CrCl3: an in-plane layered antiferromagnetic insulator. Nano Lett. 19, 3993–3998 (2019).
Li, J. et al. Intrinsic magnetic topological insulators in van der Waals layered MnBi2Te4-family materials. Sci. Adv. 5, eaaw5685 (2019).
Sun, Z. et al. Giant nonreciprocal second-harmonic generation from antiferromagnetic bilayer CrI3. Nature 572, 497–501 (2019).
Ni, Z. et al. Imaging the Néel vector switching in the monolayer antiferromagnet MnPSe3 with strain-controlled Ising order. Nat. Nanotechnol. 16, 782–781 (2021).
Gao, A. et al. Quantum metric nonlinear Hall effect in a topological antiferromagnetic heterostructure. Science 381, 181–186 (2023).
Wang, N. et al. Quantum-metric-induced nonlinear transport in a topological antiferromagnet. Nature 621, 487–492 (2023).
Kang, M. et al. Measurements of the quantum geometric tensor in solids. Nat. Phys. 21, 110–117 (2025).
Kim, S. et al. Direct measurement of the quantum metric tensor in solids. Science 388, 1050–1054 (2025).
Sala, G. et al. The quantum metric of electrons with spin-momentum locking. Science 389, 822–825 (2025).
Gao, A. et al. Layer Hall effect in a 2D topological axion antiferromagnet. Nature 595, 521–525 (2021).
Telford, E. J. et al. Layered antiferromagnetism induces large negative magnetoresistance in the van der Waals semiconductor CrSBr. Adv. Mater. 32, 2003240 (2020).
Telford, E. J. et al. Coupling between magnetic order and charge transport in a two-dimensional magnetic semiconductor. Nat. Mater. 21, 754–760 (2022).
Wu, F. et al. Quasi-1D electronic transport in a 2D magnetic semiconductor. Adv. Mater. 34, 2109759 (2022).
Wilson, N. P. et al. Interlayer electronic coupling on demand in a 2D magnetic semiconductor. Nat. Mater. 20, 1657–1662 (2021).
Cenker, J. et al. Reversible train-induced magnetic phase transition in a van der Waals magnet. Nat. Nanotechnol. 17, 256–261 (2022).
Lee, K. et al. Magnetic order and symmetry in the 2D semiconductor CrSBr. Nano Lett. 21, 3511–3517 (2021).
Tschudin, M. et al. Imaging nanomagnetism and magnetic phase transition in atomically thin CrSBr. Nat. Commun. 15, 6005 (2024).
Sun, Z. et al. Resolving and routing magnetic polymorphs in a 2D layered antiferromagnet. Nat. Mater. 24, 226–233 (2025).
Boix-Constant, C. et al. Multistep magnetization switching in orthogonally twisted ferromagnetic monolayers. Nat. Mater. 23, 212–218 (2024).
Jo, J. et al. Local control of superconductivity in a NbSe2/CrSBr van der Waals heterostructure. Nat. Commun. 14, 7253 (2023).
Yang, B. et al. Electrostatically controlled spin polarization in graphene-CrSBr magnetic proximity heterostructures. Nat. Commun. 15, 4459 (2024).
Gabor, N. M. et al. Hot carrier-assisted intrinsic photoresponse in graphene. Science 334, 648–652 (2011).
Ideue, T. et al. Bulk rectification effect in a polar semiconductor. Nat. Phys. 13, 578–583 (2017).
Watanabe, H. & Yanase, Y. Nonlinear electric transport in odd-parity magentic multipole systems: application to Mn-based compounds. Phys. Rev. Res. 2, 043081 (2020).
Das, K., Zhao, Y. & Yan, B. Surface-dominated quantum-metric-induced nonlinear transport in the layered antiferromagnet CrSBr. Nano Lett. 25, 9189–9196 (2025).
Scheie, A. et al. Spin waves and magnetic exchange hamiltonian in CrSBr. Adv. Sci. 9, 2202467 (2022).
Novoselov, K. S. et al. Two-dimensional atomic crystals. Proc. Natl Acad. Sci. USA 102, 10451–10453 (2005).
Sunku, S. S. et al. Photonic crystals for nano-light in moiré graphene superlattices. Science 362, 1153–1156 (2018).
Dong, Y. et al. Layer photovoltaic effect in a two-dimensional parity-time symmetric antiferromagnet. figshare https://doi.org/10.6084/m9.figshare.31827727 (2026).