Analogy Between Periodically Driven Josephson ac Effect and Quantum Hall Effect

TL;DR

This paper draws an analogy between the periodically driven Josephson ac effect and the quantum Hall effect, suggesting both originate from one-dimensional vortex-electron dynamics and unifying their mechanisms through phase-locking behavior.

Contribution

It introduces a novel analogy linking Josephson ac effect and quantum Hall effect via vortex-electron motion and phase-locking dynamics, supported by experimental evidence.

Findings

Unified the mechanisms of IQHE and FQHE under phase-locking dynamics.

Proposed that the time-averaged frequency ratio acts as the reciprocal filling factor.

Presented experimental support for the analogy.

Abstract

The hydrodynamical phase-slippage geometry and a semi-classical Josephson-RCSJ formulism are combined to make an analogy between the periodically driven Josephson ac effect and the quantum Hall effect. Both of these two macroscopic quantum effects are postulated to be originated from the one-dimensional linear vortex-electron relative motion. The mechanisms of the quantized Hall resistance of IQHE and FQHE are unified under the phase-locking dynamics of a Josephson-like oscillation which is periodically driven by the electron wave of the coherent Hall current, with the time-averaged frequency ratio playing the role of the filling factor reciprocal. Supporting experimental evidences for this scenario as well as necessary future investigations are remarked.