Possible persistence of fractional quantum Hall effect down to ultralow fillings

Abstract

A recent theoretical study indicating that the fractional quantum Hall liquid is the ground state at $\ensuremath{\nu}=1/9$ is inconsistent with an excitonic instability of the fractional quantum Hall liquid found earlier at the same filling factor. This paper shows that, when the calculation is improved perturbatively, by allowing mixing between composite fermion Landau levels, the instability disappears. In fact, no instability occurs in our theory for filling factors as low as $\ensuremath{\nu}=1/31,$ suggesting that the fractional quantum Hall effect may be robust down to much smaller filling factors than presently believed.