A Possible Unified Semi-Classical Macroscopic Quantum Phase-Locking Picture for Quantized Steps in AC-Josephson effect and Quantum Hall Effects

It has been intriguing to notice the similarity between the quantized steps in the standard of voltage and the resistance. Although the detailed quantum mechanical theoretical frameworks of the superconductive Josephson junction and the quantized Hall effects appears to be different, these two precise standards of basic electric circuits might be considered as sharing a common base of the so-called Macroscopic quantum phase-locking phenomena. 

In this report, a semiclassical phase-locking mechanism of Resistively-Capacitively-Shunted Junction model based on Josephson relation of macroscopic quantum phase is reviewed as providing a quantization process for the rf-biased Josephson ac effect. Shapiro steps of the ac-Josephson effect can be interpreted by the phase-locking ratio of a nonlinear system. Although the detail sondensation mechanism of the superconductive system and the quantum Hall systems may be different, cooper paring for the former and topological protection for the later, a collective relative motion picture between the electrons and flux quanta was proposed to unifyingly model the steps with integer or fractional ratio for both the driven Josephson ac effect and Quantized Hall effects.