Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number
Physical Review Letters
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Möller, G., & Cooper, N. (2015). Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number. Physical Review Letters, 115 https://doi.org/10.1103/PhysRevLett.115.126401
The Harper-Hofstadter model provides a fractal spectrum containing topological bands of any integer Chern number, C. We study the many-body physics that is realized by interacting particles occupying Harper-Hofstadter bands with |C| > 1. We formulate the predictions of Chern-Simons or composite fermion theory in terms of the filling factor, v, defined as the ratio of particle density to the number of single-particle states per unit area. We show that this theory predicts a series of fractional quantum Hall states with filling factors v = r/(r|C|+1) for bosons, or v = r/(2r|C|+1) for fermions. This series includes a bosonic integer quantum Hall state (bIQHE) in |C| = 2 bands. We construct specific cases where a single band of the Harper-Hofstadter model is occupied. For these cases, we provide numerical evidence that several states in this series are realized as incompressible quantum liquids for bosons with contact interactions.
The authors acknowledge support from the Leverhulme Trust under Grant No. ECF-2011-565, from the Isaac Newton Trust, and by the Royal Society under Grant No. UF120157 (G. M.), as well as by Engineering and Physical Sciences Research Council Grants No. EP/J017639/1 and No. EP/K030094/1 (N. R. C.).
Leverhulme Trust (ECF-2011-565)
Royal Society (uf120157)
External DOI: https://doi.org/10.1103/PhysRevLett.115.126401
This record's URL: https://www.repository.cam.ac.uk/handle/1810/251111