Edge and Bulk of the Fractional Quantum Hall Liquids

Abstract

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.

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

References in corpus (3)

• Randomness at the Edge: Theory of Quantum Hall transport at filling $\nu =2/3$
• Resonant Tunneling Between Quantum Hall Edge States
• Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.

Cited by in corpus (11)

• Surface quantized anomalous Hall current and magneto-electric effect in magnetically disordered topological insulators
• Optical Responses of Chiral Majorana Edge States in Two-Dimensional Topological Superconductors
• Quantum Transport in Two-Channel Fractional Quantum Hall Edges
• Strong-coupling branching of FQHL edges
• Bulk Versus Edge in the Quantum Hall Effect
• Antidot tunneling between Quantum Hall liquids with different filling factors
• Edge Modes in the Hierarchical Fractional Quantum Hall Liquids with Coulomb Interaction
• Magnetic Response in Quantized Spin Hall Phase of Correlated Electrons
• Current and charge distributions of the fractional quantum Hall liquids with edges
• Charge and current oscillations in Fractional quantum Hall systems with edges
• The edge state network model and the global phase diagram