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Fractional quantum Hall effect in the absence of Landau levels
Open accessAbstract
It is well known that the topological phenomena with fractional excitations, the fractional quantum Hall effect, will emerge when electrons move in Landau levels. Here we show the theoretical discovery of the fractional quantum Hall effect in the absence of Landau levels in an interacting fermion model. The non-interacting part of our Hamiltonian is the recently proposed topologically non-trivial flat-band model on a checkerboard lattice. In the presence of nearest-neighbouring repulsion, we find that at 1/3 filling, the Fermi-liquid state is unstable towards the fractional quantum Hall effect. At 1/5 filling, however, a next-nearest-neighbouring repulsion is needed for the occurrence of the 1/5 fractional quantum Hall effect when nearest-neighbouring repulsion is not too strong. We demonstrate the characteristic features of these novel states and determine the corresponding phase diagram. The fractional quantum Hall effect occurs when electrons move in Landau levels. In this study, using a theoretical flat-band lattice model, the fractional quantum Hall effect is observed in the presence of repulsive interactions when the band is one third full and in the absence of Landau levels.
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Cites
Topological insulators and superconductors
Qi, X.-L., & Zhang, S.-C. (2011) · Reviews of Modern Physics · doi:10.1103/revmodphys.83.1057 · Cited by 14,394
Quantized Hall Conductance in a Two-Dimensional Periodic Potential
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Anomalous Quantum Hall Effect: An Incompressible Quantum Fluid with Fractionally Charged Excitations
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Fractional Quantization of the Hall Effect: A Hierarchy of Incompressible Quantum Fluid States
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Classification of topological quantum matter with symmetries
Chiu, C.-K., Teo, J. C. Y., Schnyder, A. P., & Ryu, S. (2016) · Reviews of Modern Physics · doi:10.1103/revmodphys.88.035005 · Cited by 2,736
Signatures of fractional quantum anomalous Hall states in twisted MoTe2
Cai, J., Anderson, E., Wang, C., Zhang, X., Liu, X., Holtzmann, W., Zhang, Y., Fan, F., Taniguchi, T., Watanabe, K., et al. (2023) · Nature · doi:10.1038/s41586-023-06289-w · Cited by 719
The Quantum Anomalous Hall Effect: Theory and Experiment
Liu, C.-X., Zhang, S.-C., & Qi, X.-L. (2016) · Annual Review of Condensed Matter Physics · doi:10.1146/annurev-conmatphys-031115-011417 · Cited by 617
Regnault, N., & Bernevig, B. A. (2011) · Physical Review X · doi:10.1103/physrevx.1.021014 · Cited by 608
Fractional Chern insulators in magic-angle twisted bilayer graphene
Xie, Y., Pierce, A. T., Park, J. M., Parker, D. E., Khalaf, E., Ledwith, P., Cao, Y., Lee, S. H., Chen, S., Forrester, P. R., et al. (2021) · Nature · doi:10.1038/s41586-021-04002-3 · Cited by 523
Metadata
- Authors
- Sheng, D. N., Gu, Z.-C., Sun, K., & Sheng, L.
- Venue
- Nature Communications
- Published
- 2011-07-12
- Volume
- 2
- Issue
- 1
- Pages
- 389-389
- ISSN
- 2041-1723 (ISSN-L)
- OpenAlex
- W2085632674
- Cited by
- 636
- References
- 5
- FWCI
- 23.81
- Type
- journal article
- Language
- en
- Open access
- hybrid
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