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 ${\nu }^{-1}$ 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 $I=e\omega /2\pi$, with $\omega$ the ac drive angular frequency. By analyzing the full quantum model at non-zero $\nu$ using perturbative and exact methods, we study the effect of quantum fluctuation on the mode-locked plateaus. For $\nu =1$ quantum fluctuations smear completely the plateaus, leaving no trace of the ac drive. For $\nu \ge 1/2$ smeared plateaus remain in the I-V curve, but are not centered at the currents $I=ne\omega /2\pi$. For $\nu <1/2$ 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.

12 pages, 8 figures, minor changes

References in corpus (2)

• Exact non-equilibrium transport through point contacts in quantum wires and fractional quantum Hall devices
• Luttinger States at the Edge

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