Theory of c-axis Josephson tunneling in d-wave superconductors

TL;DR

This paper develops a theoretical framework to analyze the temperature and angular dependence of c-axis Josephson tunneling in layered d-wave superconductors, incorporating effects like angle-dependent tunneling and Andreev scattering, aligning with experimental data.

Contribution

It introduces an extended Ambegaokar-Baratoff formalism that accounts for angle-dependent tunneling and scattering effects in d-wave superconductors.

Findings

The model explains the temperature dependence of Josephson current.

It accounts for angular variations in superfluid density.

Results are consistent with experimental measurements on cuprate superconductors.

Abstract

The temperature and angular dependence of the c-axis Josephson current and the superfluid density in layered d-wave superconductors are studied within the framework of an extended Ambegaokar-Baratoff formalism. In particular, the effects of angle-dependent tunneling matrix elements and Andreev scattering at grain boundaries are taken into account. These lead to strong corrections of the low-temperature behavior of the plasma frequency and the Josephson current. Recent c-axis measurements on the cuprate high-temperature superconductors HgBa_2CaCu_{1+\delta} and Bi_2Sr_2CaCu_2O_{8+\delta} can therefore be interpreted to be consistent with a d-wave order parameter.