Fractional quantum Hall effect in a periodic potential.

摘要: The fractional quantum Hall effect in a periodic potential or modulation of the magnetic field is studied by symmetry, topological, and Chern-Simons field-theoretic methods. With boundary conditions, conductance finite system known to be fraction whose denominator degeneracy ground state. We show that system, translational symmetry predicts varies periodically with size equals 1 for certain commensurate cases which we argue are physically representative. However, this analysis may overlook gaps due finite-size effects vanish thermodynamic limit. This possibility addressed using fermionic theory mean-field approximation