Fractional quantum Hall effect in a two-dimensional hole gas

The theory of the fractional quantum Hall effect (FQHE) is extended to the case where the Fermi level lies within the valence band of a zinc-blende semiconductor. The degenerate nature of the valence band alters the character of the single-particle states within a Landau level. We show that, neglecting Landau-level mixing, the interacting-hole Hamiltonian is equivalent to the Hamiltonian for interacting electrons in the lowest-conduction-band Landau level with an effective interaction which is dependent on the valence-band mixing. Realistic calculations for typical valence-band Landau levels yield FQHE activation energies for a hole gas in a strong field which are about 10% larger than for an electron gas at the same field strength.