Small Josephson current and product deduced by means of measurement for an inhomogeneous superconductor: Extension of the Ambegaokar - Baratoff theory

TL;DR

This paper extends the Ambegaokar-Baratoff theory to inhomogeneous high-T_c superconductors, analyzing how band filling affects Josephson current and product, and discusses experimental evidence for d-wave symmetry and flux trapping.

Contribution

It introduces a band filling-dependent extension of the Ambegaokar-Baratoff theory for inhomogeneous superconductors, linking observed Josephson effects to intrinsic properties.

Findings

Observed Josephson current is proportional to band filling factor.

Josephson product is reduced in inhomogeneous samples due to band filling.

Intrinsic superconducting gap estimated between 4 and 10 meV.

Abstract

For an inhomogeneous high-T_c superconductor, band-filling dependence of Josephson current and Josephson product is deduced at T=0 K by means of measurement; this is an extension of Ambegaokar-Baratoff Josephson current and product. The observed Josephson current, J_{obs}, is given by J_{obs}={\rho}J_i, where 0<\rho<=1 is band filling (or local density). When \rho=1, J_{obs} = J_i is the intrinsic supercurrent occurring by Cooper pair. When 0<\rho<1, J_{obs} is an average of J_i over the measurement region and is the effect of measurement. The observed Ambegaokar-Baratoff Josephson product, based on the s-wave theory, is given by J_{obs}R_n =({\pi}/{2})(\rho\triangle_i), where \triangle_i is the intrinsic superconducting gap and small, which results in small Josephson products observed by the experiments. The intrinsic gap, 4<{\triangle_i}<10 meV, is analyzed from the Josephson-product data of BSCCO. In addition, the triple-{\pi}-junction experiments, observing the half-flux quantum ({\Phi_0}/2) as evidence of d-wave symmetry, are discussed by using means of measurement. Comments on a flux trap of the magnetic modulation experiment using Pb-YBCO dc SQUIDs are also given. Author's thought is given on the angle dependence of $J_c$ measured in whisker.