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 $ν^{-1}$ 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 semi-classical limit which ignores electron tunnelling, this model exhibits mode-locking, which corresponds to current plateaus in the I-V curve at integer multiples of $I= eω/2π$, with $ω$ the ac drive angular frequency. By analyzing the full quantum model at non-zero $ν$ using perturbative and exact methods, we study the effect of quantum fluctuation on the mode-locked plateaus. For $ν=1$ quantum fluctuations smear completely the plateaus, leaving no trace of the ac drive. For $ν\ge 1/2$ smeared plateaus remain in the I-V curve, but are not centered at the currents $I=n e ω/2π$. For $ν< 1/2$ rounded plateaus centered around the quantized current values are found. The possibility of using mode locking in FQHE point contacts as a current-to-frequency standard is discussed.