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arXiv · 1504.06623

Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number

Gunnar Möller·Nigel R. Cooper
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Abstract

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, $\nu$, 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 $\nu = r/(r|C| +1)$ for bosons, or $\nu = r/(2r|C| +1)$ 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.

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Gunnar Möller, Nigel R. Cooper. 2015-04-24. Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number. https://doi.org/10.1103/physrevlett.115.126401

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