Consideration of ac Josephson Effect in Fractional Quantum Hall States

TL;DR

This paper investigates the ac Josephson effect in fractional quantum Hall states with a novel device structure, revealing how the transfer charge depends on the fractional filling factor and providing insights into the quantum Hall wave functions.

Contribution

It introduces a new quantum Hall device with a variable thickness region to study the ac Josephson effect and links the transfer charge to the wave function type of FQHS.

Findings

The voltage steps relate to the transfer charge Q and oscillation frequency f.

Q depends on the fractional filling factor nu and wave function type.

Observation of the effect clarifies the structure of FQHS.

Abstract

The ac Josephson effect phenomenon is studied in fractional quantum Hall states (FQHS). Usual quantum Hall devices have an electron layer of uniform thickness. We consider a new quantum Hall device. The device has a narrow part that is vertical to the direction of the current. The narrow part has a smaller electron layer thickness than in the other part. The ac Josephson effect might be observed when the magnetic field or the electric current is modulated by an oscillation with a constant frequency value f. Steps of the voltage appear when an electric current exceed a threshold value. The step value V is related to the transfer charge Q as V=(2 pi hbar f)/Q. We examine how the value of the transfer charge Q depends on the fractional filling factor nu. The nu - dependence of Q is affected by the wave function of the fractional quantum Hall state. We classify the value of Q according to the wave function type. Accordingly, observation of the ac Josephson effect in FQHS clarifies the structure of the fractional quantum Hall states.