Boundary degrees of freedom in fractional quantum Hall effect: Excitations on common boundary of two samples

TL;DR

This paper derives the boundary action for fermion Chern-Simons theory in quantum Hall effects, computing bulk and edge responses, and revealing how boundary currents depend on differences in Chern-Simons couplings.

Contribution

It provides a derivation of boundary actions and edge currents in quantum Hall systems without ad hoc assumptions, highlighting the role of boundary degrees of freedom.

Findings

Derived boundary action using Carlip's method

Computed bulk and edge current responses to electric fields

Found boundary Hall current proportional to coupling differences

Abstract

Using the Carlip's method we have derived the boundary action for the fermion Chern-Simons theory of quantum Hall effects on a planar region with a boundary. We have computed both the bulk and edge responses of currents to the external electric field. From this we obtain the well-known anomaly relation and the boundary Hall current without introducing any ad hoc assumptions such as the chirality condition. In addition, the edge current on the common boundary of two samples is found to be proportional to the difference between Chern-Simons coupling strengths.