FRACTIONAL QUANTUM HALL-EFFECT IN A PERIODIC POTENTIAL

The fractional quantum Hall effect in a periodic potential or modulati on of the magnetic field is studied by symmetry, topological, and Chem -Simons field-theoretic methods. With periodic boundary conditions, th e Hall conductance in a finite system is known to be a fraction whose denominator is the degeneracy of the ground state. We show that in a f inite system, translational symmetry predicts a degeneracy that varies periodically with system size and equals 1 for certain commensurate c ases which we argue are physically representative. However, this analy sis may overlook gaps due to finite-size effects that vanish in the th ermodynamic limit. This possibility is addressed using a fermionic Che rn-Simons field theory in the mean-field approximation. In addition to solutions describing the usual Laughlin or Jain states whose properti es are only weakly modified by the periodic background, we also find s olutions whose existence depends on the presence of the background. In these incompressible states, the Hall conductance is a fraction not e qual to the filling factor, and its denominator is the same as that of the fractional charge and statistics of the elementary quasiparticle excitations.