title: Fractional Chern Insulators in Harper-Hofstadter Bands with Higher Chern Number.
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 ν, 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 ν=r/(r|C|+1) for bosons, or ν=r/(2r|C|+1) for fermions. This series includes a bosonic integer quantum Hall state 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.
authors.affiliation: TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
authors.forename: Gunnar
authors.initials: G
authors.lastname: Möller
authors.affiliation: TCM Group, Cavendish Laboratory, University of Cambridge, Cambridge CB3 0HE, United Kingdom.
authors.forename: Nigel R
authors.initials: NR
authors.lastname: Cooper