• Barber, M. E., Ma, E. Y. & Shen, Z.-X. Microwave impedance microscopy and its application to quantum materials. Nat. Rev. Phys. 4, 61–74 (2022).

    Article 

    Google Scholar
     

  • Tsui, D. C., Stormer, H. L. & Gossard, A. C. Two-dimensional magnetotransport in the extreme quantum limit. Phys. Rev. Lett. 48, 1559–1562 (1982).

    Article 
    CAS 

    Google Scholar
     

  • Laughlin, R. B. Anomalous quantum Hall effect: an incompressible quantum fluid with fractionally charged excitations. Phys. Rev. Lett. 50, 1395 (1983).

    Article 

    Google Scholar
     

  • Halperin, B. I. Statistics of quasiparticles and the hierarchy of fractional quantized Hall states. Phys. Rev. Lett. 52, 1583 (1984).

    Article 

    Google Scholar
     

  • Arovas, D., Schrieffer, J. R. & Wilczek, F. Fractional statistics and the quantum Hall effect. Phys. Rev. Lett. 53, 722 (1984).

    Article 

    Google Scholar
     

  • Stern, A. Anyons and the quantum Hall effect—a pedagogical review. Ann. Phys. 323, 204–249 (2008).

    Article 
    MathSciNet 
    CAS 

    Google Scholar
     

  • Goldman, V. & Su, B. Resonant tunneling in the quantum Hall regime: measurement of fractional charge. Science 267, 1010–1012 (1995).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Martin, J. et al. Localization of fractionally charged quasi-particles. Science 305, 980–983 (2004).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Radu, I. P. et al. Quasi-particle properties from tunneling in the v = 5/2 fractional quantum Hall state. Science 320, 899–902 (2008).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • De-Picciotto, R. et al. Direct observation of a fractional charge. Physica B 249, 395–400 (1998).

    Article 

    Google Scholar
     

  • Bartolomei, H. et al. Fractional statistics in anyon collisions. Science 368, 173–177 (2020).

    Article 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Pascher, N. et al. Imaging the conductance of integer and fractional quantum Hall edge states. Phys. Rev. X 4, 011014 (2014).


    Google Scholar
     

  • Chang, A. Chiral Luttinger liquids at the fractional quantum Hall edge. Rev. Mod. Phys. 75, 1449 (2003).

    Article 
    MathSciNet 
    CAS 

    Google Scholar
     

  • Nayak, C., Simon, S. H., Stern, A., Freedman, M. & Sarma, S. D. Non-Abelian anyons and topological quantum computation. Rev. Mod. Phys. 80, 1083 (2008).

    Article 
    MathSciNet 
    CAS 

    Google Scholar
     

  • Ashoori, R., Stormer, H., Pfeiffer, L., Baldwin, K. & West, K. Edge magnetoplasmons in the time domain. Phys. Rev. B 45, 3894 (1992).

    Article 
    CAS 

    Google Scholar
     

  • Stuhl, B., Lu, H.-I., Aycock, L., Genkina, D. & Spielman, I. Visualizing edge states with an atomic Bose gas in the quantum Hall regime. Science 349, 1514–1518 (2015).

    Article 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Yao, R. et al. Observation of chiral edge transport in a rapidly rotating quantum gas. Nature https://doi.org/10.1038/s41567-024-02617-7 (2024).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Mancini, M. et al. Observation of chiral edge states with neutral fermions in synthetic Hall ribbons. Science 349, 1510–1513 (2015).

    Article 
    MathSciNet 
    CAS 
    PubMed 

    Google Scholar
     

  • Wang, Z., Chong, Y., Joannopoulos, J. D. & Soljačić, M. Observation of unidirectional backscattering-immune topological electromagnetic states. Nature 461, 772–775 (2009).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Lai, K. et al. Imaging of Coulomb-driven quantum Hall edge states. Phys. Rev. Lett. 107, 176809 (2011).

    Article 
    PubMed 

    Google Scholar
     

  • Cui, Y.-T. et al. Unconventional correlation between quantum Hall transport quantization and bulk state filling in gated graphene devices. Phys. Rev. Lett. 117, 186601 (2016).

    Article 
    PubMed 

    Google Scholar
     

  • Yacoby, A., Hess, H., Fulton, T., Pfeiffer, L. & West, K. Electrical imaging of the quantum Hall state. Solid State Commun. 111, 1–13 (1999).

    Article 
    CAS 

    Google Scholar
     

  • Suddards, M., Baumgartner, A., Henini, M. & Mellor, C. J. Scanning capacitance imaging of compressible and incompressible quantum Hall effect edge strips. New J. Phys. 14, 083015 (2012).

    Article 

    Google Scholar
     

  • Shi, Y. et al. Imaging quantum spin Hall edges in monolayer WTe2. Sci. Adv. 5, eaat8799 (2019).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Allen, M. et al. Visualization of an axion insulating state at the transition between 2 chiral quantum anomalous Hall states. Proc. Natl Acad. Sci. 116, 14511–14515 (2019).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Cai, J. et al. Signatures of fractional quantum anomalous Hall states in twisted MoTe2. Nature 622, 63–68 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Zeng, Y. et al. Thermodynamic evidence of fractional Chern insulator in moiré MoTe2. Nature 622, 69–73 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Park, H. et al. Observation of fractionally quantized anomalous Hall effect. Nature 622, 74–79 (2023).

    Article 
    CAS 
    PubMed 

    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).

    CAS 

    Google Scholar
     

  • Lu, Z. et al. Fractional quantum anomalous Hall effect in multilayer graphene. Nature 626, 759–764 (2024).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Uri, A. et al. Mapping the twist-angle disorder and Landau levels in magic-angle graphene. Nature 581, 47–52 (2020).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Chu, Z. et al. Unveiling defect-mediated carrier dynamics in monolayer semiconductors by spatiotemporal microwave imaging. Proc. Natl Acad. Sci. 117, 13908–13913 (2020).

    Article 
    CAS 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Cui, Y.-T., Ma, E. Y. & Shen, Z.-X. Quartz tuning fork based microwave impedance microscopy. Rev. Sci. Instrum. 87, 063711 (2016).

    Article 
    PubMed 

    Google Scholar
     

  • Huang, X. et al. Correlated insulating states at fractional fillings of the WS2/WSe2 moiré lattice. Nat. Phys. 17, 715–719 (2021).

    Article 
    CAS 

    Google Scholar
     

  • Ji, Z. et al. Harnessing excitons at the nanoscale–photoelectrical platform for quantitative sensing and imaging. Preprint at https://arxiv.org/abs/2311.04211 (2023).

  • 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).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Goldman, H., Reddy, A. P., Paul, N. & Fu, L. Zero-field composite Fermi liquid in twisted semiconductor bilayers. Phys. Rev. Lett. 131, 136501 (2023).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Regan, E. C. et al. Mott and generalized Wigner crystal states in WSe2/WS2 moiré superlattices. Nature 579, 359–363 (2020).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Tang, Y. et al. Simulation of Hubbard model physics in WSe2/WS2 moiré superlattices. Nature 579, 353–358 (2020).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Li, H. et al. Imaging two-dimensional generalized Wigner crystals. Nature 597, 650–654 (2021).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Wang, T. et al. Probing the edge states of Chern insulators using microwave impedance microscopy. Phys. Rev. B 108, 235432 (2023).

    Article 
    CAS 

    Google Scholar
     

  • Lee, D.-H., Wang, Z. & Kivelson, S. Quantum percolation and plateau transitions in the quantum Hall effect. Phys. Rev. Lett. 70, 4130 (1993).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Wen, X.-G. Theory of the edge states in fractional quantum Hall effects. Int. J. Mod. Phys. B 6, 1711–1762 (1992).

    Article 
    MathSciNet 
    CAS 

    Google Scholar
     

  • Zülicke, U., MacDonald, A. & Johnson, M. Observability of counterpropagating modes at fractional quantum Hall edges. Phys. Rev. B 58, 13778 (1998).

    Article 

    Google Scholar
     

  • Sabo, R. et al. Edge reconstruction in fractional quantum Hall states. Nat. Phys. 13, 491–496 (2017).

    Article 
    CAS 

    Google Scholar
     

  • Kane, C., Fisher, M. P. & Polchinski, J. Randomness at the edge: theory of quantum Hall transport at filling ν=2/3. Phys. Rev. Lett. 72, 4129 (1994).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Redekop, E. et al. Direct magnetic imaging of fractional Chern insulators in twisted MoTe2 with a superconducting sensor. Preprint at https://arxiv.org/abs/2405.10269 (2024).

  • Dutta, B. et al. Distinguishing between non-abelian topological orders in a quantum Hall system. Science 375, 193–197 (2022).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Direct observation of anyonic braiding statistics. Nat. Phys. 16, 931–936 (2020).

    Article 
    CAS 

    Google Scholar
     

  • Meir, Y. Composite edge states in the ν=2/3 fractional quantum Hall regime. Phys. Rev. Lett. 72, 2624 (1994).

    Article 
    CAS 
    PubMed 

    Google Scholar
     

  • Nakamura, J., Liang, S., Gardner, G. C. & Manfra, M. J. Fabry-Pérot interferometry at the ν = 2/5 fractional quantum Hall state. Phys. Rev. X 13, 041012 (2023).

    CAS 

    Google Scholar
     

  • Santos, L. H., Cano, J., Mulligan, M. & Hughes, T. L. Symmetry-protected topological interfaces and entanglement sequences. Phys. Rev. B 98, 075131 (2018).

    Article 
    CAS 

    Google Scholar
     

  • Crépel, V., Claussen, N., Estienne, B. & Regnault, N. Model states for a class of chiral topological order interfaces. Nat. Commun. 10, 1861 (2019).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Crépel, V., Claussen, N., Regnault, N. & Estienne, B. Microscopic study of the Halperin–Laughlin interface through matrix product states. Nat. Commun. 10, 1860 (2019).

    Article 
    PubMed 
    PubMed Central 

    Google Scholar
     

  • Ji, Z. et al. Original data for “Local probe of bulk and edge states in a fractional Chern insulator”. Dryad https://doi.org/10.5061/dryad.9p8cz8ws0 (2024).



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