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

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

1997-07-17

arxiv.org/abs/cond-mat/9707177v1

Physics

Condensed Matter

20 pages, uses revtex

Scientific paper

10.1103/PhysRevB.57.7149

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.

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