Shapiro steps in Josephson junctions with alternating critical current density

TL;DR

This paper provides a theoretical analysis of Shapiro steps in Josephson junctions with alternating critical current density, deriving formulas for step widths and applying the approach to various heterostructures.

Contribution

It introduces explicit analytical formulas for Shapiro step widths in short junctions with alternating critical current density and develops a coarse-graining method for complex heterostructures.

Findings

Analytical formulas for first integer and half-integer Shapiro step widths.

Coarse-graining approach for asymmetric grain boundaries and heterostructures.

Application to YBCO thin films and superconductor-ferromagnet-superconductor junctions.

Abstract

We treat theoretically Shapiro steps in tunnel Josephson junctions with spatially alternating critical current density. Explicit analytical formulas for the width of the first integer (normal) and half-integer (anomalous) Shapiro steps are derived for short junctions. We develop coarse-graining approach, which describes Shapiro steps in the voltage-current curves of the asymmetric grain boundaries in YBCO thin films and different superconductor-ferromagnet-superconductor Josephson-type heterostructures.