Upper bound on the Andreev states induced second harmonic in the Josephson coupling of YBa2Cu3O7−δ/Nb junctions from experiment and numerical simulations

Theory predicts that d-wave superconductivity induces a significant second harmonic J2 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 YBa2Cu3O7−δ 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 J2. This result combined with extensive numerical simulations put an upper bound on the ZES-induced J2 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 J2 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 J2.