Coulomb blockade in hierarchical quantum Hall droplets

ANDREA CAPPELLI , LACHEZAR S GEORGIEV , GUILLERMO R ZEMBA

JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL

IOP PUBLISHING LTD

Año: 2009 vol. 42 p. 222001 - 222004

1751-8113

The degeneracy of energy levels in a quantum dot of Hall fluid, leading to conductance peaks, can be readily derived from the partition functions of conformal field theory. Their complete expressions can be found for Hall states with both Abelian and non-Abelian statistics, upon adapting known results for the annulus geometry. We analyze the Abelian states with hierarchical filling fractions, ν = m/(mp ± 1), and find a non-trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, which is due to the extended symmetry of the m-folded edge. Experimental tests of the multiplicity can shed more light on the dynamics of this composite edge.