Electric Field Effect on the Fractional Quantum Hall Conductivity

We have studied the effect of an external electric field on the dc fractional quantum Hall conductivity of a two-dimensional system with the dynamic structure function in the single-mode approximation. In analogy with the integral quantum Hall effect and euperconductivity, a gap-dependent critical electric current J_c, also exists in the case of fracctional quantum Hall conduction, above which is the maximum current for system to maintain superfluidity. We also find that, depending on the gap width and the phonon velocity, phonon may or may not contribute to the conductivity even at a finite lattice temperature, in agreement with experiments.