Mode-Locking in Quantum-Hall-Effect Point Contacts

TL;DR

This paper investigates how an ac drive influences the current-voltage characteristics of fractional Quantum Hall effect point contacts, revealing quantum fluctuations' impact on mode-locking phenomena and potential applications as a current-to-frequency standard.

Contribution

It extends the classical mode-locking model to the quantum regime in fractional Quantum Hall systems, analyzing quantum fluctuations' effects on current plateaus in the I-V characteristics.

Findings

Quantum fluctuations smear mode-locking plateaus at ν=1.

Smeared plateaus persist for ν ≥ 1/2 but shift from quantized values.

Rounded plateaus appear for ν < 1/2, centered around quantized currents.

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 $I=n e \omega /2\pi$. 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.