Edge states in the fractional-quantum-Hall-effect regime

A finite-two-dimensional electron gas with N full Landau levels has N branches of edge states which cross the Fermi level. In this Letter we show that in the fractional-quantum-Hall-effect regime there can be many branches of edge states for a single partly filled Landau level. The ith branch can be associated with a fractional charge, ${\mathrm{ef}}_i$, and ${\Sigma }_i$ $f_i$ equals the Landau-level filling factor. The set of edge-state charges at a particular filling factor directly reflects the hierarchical structure of the incompressible ground state which occurs at the filling factor.