Finkler, A. et al. Self-aligned nanoscale SQUID on a tip. Nano Lett. 10, 1046–1049 (2010).
Google Scholar
Vasyukov, D. et al. A scanning superconducting quantum interference device with single electron spin sensitivity. Nat. Nanotechnol. 8, 639–644 (2013).
Google Scholar
Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).
Google Scholar
Xu, F. et al. Observation of integer and fractional quantum anomalous Hall effects in twisted bilayer MoTe2. Phys. Rev. X 13, 031037 (2023).
Google Scholar
Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).
Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).
Google Scholar
Uri, A. et al. Mapping the twist-angle disorder and Landau levels in magic-angle graphene. Nature 581, 47–52 (2020).
Google Scholar
Spanton, E. M. et al. Observation of fractional Chern insulators in a van der Waals heterostructure. Science 360, 62–66 (2018).
Google Scholar
Cao, Y. et al. Correlated insulator behaviour at half-filling in magic-angle graphene superlattices. Nature 556, 80–84 (2018).
Google Scholar
Chen, G. et al. Evidence of a gate-tunable Mott insulator in a trilayer graphene moiré superlattice. Nat. Phys. 15, 237–241 (2019).
Google Scholar
Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).
Google Scholar
Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).
Google Scholar
Wang, L. et al. Correlated electronic phases in twisted bilayer transition metal dichalcogenides. Nat. Mater. 19, 861–866 (2020).
Google Scholar
Shimazaki, Y. et al. Strongly correlated electrons and hybrid excitons in a moiré heterostructure. Nature 580, 472–477 (2020).
Google Scholar
Xu, Y. et al. Correlated insulating states at fractional fillings of moiré superlattices. Nature 587, 214–218 (2020).
Google Scholar
Sharpe, A. L. et al. Emergent ferromagnetism near three-quarters filling in twisted bilayer graphene. Science 365, 605–608 (2019).
Google Scholar
Serlin, M. et al. Intrinsic quantized anomalous Hall effect in a moiré heterostructure. Science 367, 900–903 (2020).
Google Scholar
Chen, G. et al. Tunable correlated Chern insulator and ferromagnetism in a moiré superlattice. Nature 579, 56–61 (2020).
Google Scholar
Li, T. et al. Quantum anomalous Hall effect from intertwined moiré bands. Nature 600, 641–646 (2021).
Google Scholar
Anderson, E. et al. Programming correlated magnetic states with gate-controlled moiré geometry. Science 381, 325–330 (2023).
Google Scholar
Xie, Y. et al. Fractional Chern insulators in magic-angle twisted bilayer graphene. Nature 600, 439–443 (2021).
Google Scholar
Ji, Z. et al. Local probe of bulk and edge states in a fractional Chern insulator. Preprint at https://arxiv.org/abs/2404.07157 (2024).
Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).
Google Scholar
Li, H., Kumar, U., Sun, K. & Lin, S.-Z. Spontaneous fractional Chern insulators in transition metal dichalcogenide moiré superlattices. Phys. Rev. Res. 3, L032070 (2021).
Google Scholar
Dong, Z., Patri, A. S. & Senthil, T. Theory of quantum anomalous Hall phases in pentalayer rhombohedral graphene moiré structures. Preprint at https://arxiv.org/abs/2311.03445 (2023).
Dong, Z., Patri, A. S. & Senthil, T. Stability of anomalous Hall crystals in multilayer rhombohedral graphene. Preprint at https://arxiv.org/abs/2403.07873 (2024).
Wang, C. et al. Fractional Chern insulator in twisted bilayer MoTe2. Phys. Rev. Lett. 132, 036501 (2024).
Google Scholar
Yu, J. et al. Fractional Chern insulators versus nonmagnetic states in twisted bilayer MoTe2. Phys. Rev. B 109, 045147 (2024).
Google Scholar
Morales-Durán, N., Wei, N., Shi, J. & MacDonald, A. H. Magic angles and fractional Chern insulators in twisted homobilayer transition metal dichalcogenides. Phys. Rev. Lett. 132, 096602 (2024).
Jia, Y. et al. Moire fractional Chern insulators. I. First-principles calculations and continuum models of twisted bilayer MoTe2. Phys. Rev. B 109, 205121 (2024).
Google Scholar
Sheng, D. N., Reddy, A. P., Abouelkomsan, A., Bergholtz, E. J. & Fu, L. Quantum anomalous Hall crystal at fractional filling of moiré superlattices. Phys. Rev. Lett. 133, 066601 (2024).
Dong, J. et al. Anomalous Hall crystals in rhombohedral multilayer graphene. I. Interaction-driven Chern bands and fractional quantum Hall states at zero magnetic field. Preprint at https://arxiv.org/abs/2311.05568 (2023).
Soejima, T. et al. Anomalous Hall crystals in rhombohedral multilayer graphene. II. General mechanism and a minimal model. Preprint at https://arxiv.org/abs/2403.05522 (2024).
Goldman, H., Reddy, A. P., Paul, N. & Fu, L. Zero-field composite Fermi liquid in twisted semiconductor bilayers. Phys. Rev. Lett. 131, 136501 (2023).
Google Scholar
Anahory, Y. et al. SQUID-on-tip with single-electron spin sensitivity for high-field and ultra-low temperature nanomagnetic imaging. Nanoscale 12, 3174–3182 (2020).
Google Scholar
Dong, J., Wang, J., Ledwith, P. J., Vishwanath, A. & Parker, D. E. Composite Fermi liquid at zero magnetic field in twisted MoTe2. Phys. Rev. Lett. 131, 136502 (2023).
Google Scholar
Jain, J. K. Composite-fermion approach for the fractional quantum Hall effect. Phys. Rev. Lett. 63, 199–202 (1989).
Google Scholar
Deilmann, T., Krüger, P. & Rohlfing, M. Ab initio studies of exciton g factors: monolayer transition metal dichalcogenides in magnetic fields. Phys. Rev. Lett. 124, 226402 (2020).
Google Scholar
Woźniak, T., Faria Junior, P. E., Seifert, G., Chaves, A. & Kunstmann, J. Exciton g factors of van der Waals heterostructures from first-principles calculations. Phys. Rev. B 101, 235408 (2020).
Google Scholar
Robert, C. et al. Measurement of conduction and valence bands g-factors in a transition metal dichalcogenide monolayer. Phys. Rev. Lett. 126, 067403 (2021).
Google Scholar
Morf, R. & Halperin, B. I. Monte Carlo evaluation of trial wave functions for the fractional quantized Hall effect: disk geometry. Phys. Rev. B 33, 2221–2246 (1986).
Google Scholar
Yang, F. et al. Experimental determination of the energy per particle in partially filled Landau levels. Phys. Rev. Lett. 126, 156802 (2021).
Google Scholar
Grover, S. et al. Chern mosaic and Berry-curvature magnetism in magic-angle graphene. Nat. Phys. 18, 885–892 (2022).
Google Scholar
Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).
Google Scholar
Huber, M. E. et al. DC SQUID series array amplifiers with 120 MHz bandwidth. IEEE Trans. Appl. Supercond. 11, 1251–1256 (2001).
Google Scholar
Tschirhart, C. L. et al. Imaging orbital ferromagnetism in a moiré Chern insulator. Science 372, 1323–1327 (2021).
Google Scholar
Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2. Dryad https://doi.org/10.5061/dryad.0zpc86769 (2024).
Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2. Zenodo https://doi.org/10.5281/zenodo.13621665 (2024).
