Universality Lost: Relation between quantizations of the Hall conductance and the edge exponents in fractional quantum Hall effect

TL;DR

This paper explores how non-universal edge exponents in fractional quantum Hall systems imply a breakdown of the universality of Hall conductance, highlighting the connection between edge state properties and bulk conductance.

Contribution

It demonstrates the link between edge exponent non-universality and Hall conductance non-universality using examples with backward moving neutral modes.

Findings

Non-universality of edge exponents correlates with non-universal Hall conductance.

Edge reconstruction and composite fermions with reverse flux lead to non-universal behaviors.

The study emphasizes the importance of edge state details in quantum Hall measurements.

Abstract

We note an implication of chiral Luttinger liquid based edge state description of the fractional quantum Hall effect. By considering several examples that involve backward moving neutral modes, arising from either composite fermions with reverse flux attached or edge reconstruction, we show that non-universality of the edge exponent implies non-universality of the Hall conductance, as measured in the two-terminal conductance.