Near-field optical mapping of quantum Hall edge states.

We report on the mapping of quantum-Hall edge states by quasiresonant photovoltage measurements using a near-field scanning optical microscope. We have observed fine structures near sample edges that shift inward with an increase in magnetic field in accordance with the shift of the positions of the quantum-Hall edge states. We have found a transition from the weak disorder regime where compressible-incompressble strips are visible to the strong disorder regime where fluctuations smear out incompressible strips.