Upper bound on the Andreev states induced second harmonic in the Josephson coupling ofYBa2Cu3O7−δ/Nbjunctions from experiment and numerical simulations

Abstract

Theory predicts that $d$-wave superconductivity induces a significant second harmonic ${J}_{2}$ in the Josephson current, as a result of zero-energy Andreev states (ZES) formed at the junction interface. Consequently, anomalies such as half-integer Shapiro steps and signatures of period doubling of the dc Josephson current versus magnetic field should be observed. We performed experiments on junctions between untwinned $d$-wave ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{7\ensuremath{-}\ensuremath{\delta}}$ and Nb and found no trace of such anomalies although clear evidence of Andreev states formation is provided. These findings do not lead to an observable ${J}_{2}$. This result combined with extensive numerical simulations put an upper bound on the ZES-induced ${J}_{2}$ of about 0.1% from the first harmonic in the Josephson current for tunneling into the [010] direction and of about 2% for tunneling close to the [110] direction. Our results suggest strong ${J}_{2}$ suppression by diffusive scattering, which is possibly due to nanoscale interface roughness. This is important for proposed (quantum)-electronic device concepts based on the expectance of ${J}_{2}$.