Edge and Bulk of the Fractional Quantum Hall Liquids

Details Edge and Bulk of the Fractional Quantum Hall Liquids Edge and Bulk of the Fractional Quantum Hall Liquids

1995-05-26

arxiv.org/abs/cond-mat/9505134v1

Physics

Condensed Matter

13 pages, REVTEX, one figure appended as a postscript file

Scientific paper

10.1103/PhysRevLett.75.4294

An effective Chern-Simons theory for the Abelian quantum Hall states with edges is proposed to study the edge and bulk properties in a unified fashion. We impose a condition that the currents do not flow outside the sample. With this boundary condition, the action remains gauge invariant and the edge modes are naturally derived. We find that the integer coupling matrix $K$ should satisfy the condition $\sum_I(K^{-1})_{IJ} = \nu/m$ ($\nu$: filling of Landau levels, $m$: the number of gauge fields ) for the quantum Hall liquids. Then the Hall conductance is always quantized irrespective of the detailed dynamics or the randomness at the edge.

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