Giant Shapiro Steps in Josephson Arrays: Analytical Results

TL;DR

This paper analytically investigates giant Shapiro steps in frustrated Josephson arrays under combined DC and AC currents, deriving expressions for step widths and explaining differences between fractional and integer steps.

Contribution

It introduces generalized ansatz solutions for driven Josephson arrays and derives analytical expressions for Shapiro step widths at specific frequencies.

Findings

Derived formulas for Shapiro step widths at f=1/2 and f=1/3.

Identified the role of vertical supercurrent in step behavior.

Explained qualitative differences between fractional and integer steps.

Abstract

We study two-dimensional frustrated Josephson arrays driven by a combined DC plus AC current. We propose {\it ansatz} solutions that are a generalization of the solutions obtained in the DC case by Marino and Halsey (PRB {\bf 50}, 6289 (1994)). Using these solutions we derive expressions for the Shapiro step widths for $f=1/2$ and $f=1/3$ for the first few winding numbers. We show that the qualitative difference in the behaviors of the fractional and integer steps is related to the relative size of the vertical supercurrent with respect to the normal current.