Edge Modes in the Hierarchical Fractional Quantum Hall Liquids with Coulomb Interaction

Edge modes are studied for the hierarchical fractional quantum Hall liquids (FQHL) by treating the edge and bulk in a unified fashion. Within the RPA treatment of the composite boson effective theory with Coulomb interaction, one edge magneto-plasmon is shown to be the eigen-mode of the system. This mode decays algebraically perpendicular to the edge. All the other modes decay faster than power-law, and correspond to the neutral modes. However these neutral modes generally couple with the electromagnetic field within the magnetic length from the edge. The time-of-flight experiment in the $\nu=2/3$ FQHL is discussed in terms of these results.