Coulomb Blockade in Hierarchical Quantum Hall Droplets

TL;DR

This paper explores the Coulomb blockade phenomena in hierarchical quantum Hall droplets, deriving conductance peak patterns from conformal field theory and highlighting the role of edge symmetry in peak multiplicities.

Contribution

It provides a detailed analysis of conductance peaks in hierarchical Abelian quantum Hall states using conformal field theory, revealing characteristic multiplicities linked to edge symmetries.

Findings

Identified non-trivial conductance peak patterns in hierarchical quantum Hall states.

Discovered that peak multiplicities are due to extended edge symmetries.

Proposed experimental tests to explore edge dynamics.

Abstract

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, \nu=m/(mp \pm 1), and find a non trivial pattern of conductance peaks. In particular, each one of them occurs with a characteristic multiplicity, that 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.