Mode locking in quantum-Hall-effect point contacts.

Abstract

We study the effect of an ac drive on the current-voltage (I-V) characteristics of a tunnel junction between two fractional quantum Hall fluids at filling ${\ensuremath{\nu}}^{\mathrm{\ensuremath{-}}1}$ an odd integer. Within the chiral Luttinger-liquid model of edge states, the point-contact dynamics is described by a driven damped quantum mechanical pendulum. In a semiclassical limit which ignores electron tunneling, this model exhibits mode locking, which corresponds to current plateaus in the I-V curve at integer multiples of I=e\ensuremath{\omega}/2\ensuremath{\pi}, with \ensuremath{\omega} the ac drive angular frequency. By analyzing the full quantum model at nonzero \ensuremath{\nu} using perturbative and exact methods, we study the effect of quantum fluctuation on the mode-locked plateaus. For \ensuremath{\nu}=1, quantum fluctuations smear completely the plateaus, leaving no trace of the ac drive. For \ensuremath{\nu}\ensuremath{\geqslant}1/2 smeared plateaus remain in the I-V curve, but are not centered at the currents I=ne\ensuremath{\omega}/2\ensuremath{\pi}. For \ensuremath{\nu}1/2 rounded plateaus centered around the quantized current values are found. The possibility of using mode locking in fractional quantum-Hall-effect point contacts as a current-to-frequency standard is discussed. \textcopyright{} 1996 The American Physical Society.