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Hamiltonian Theory of Fractional Chern Bands

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It has been known for some time that a system with a filled band will have an integer quantum Hall conductance equal to its Chern number, a topological index associated with the band. While this is true for a system in a magnetic field with filled Landau Levels, even a system in zero external field can exhibit the QHE if its band has a Chern number. I review this issue and discuss a more recent question of whether a partially filled Chern band can exhibit the Fractional QHE . I describe the work done with Ganpathy Murthy, in which we show how composite fermions, which were so useful in explaining the usual FQHE , can be introduced here and with equal success by adapting our Hamiltonian Theory of CFs developed for the FQHE in the continuum.

This talk is part of the Theory of Condensed Matter series.

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