Geometric Scaling of the Current-Phase Relation of Niobium Nanobridge Junctions

The nanobridge junction (NBJ) is a type of Josephsonjunction thatis advantageous for the miniaturization of superconducting circuits.However, the current-phase relation (CPR) of the NBJ usuallydeviates from a sinusoidal function, which has been explained by asimplified model with correlation only to its effective length. Here,we investigated both measured and calculated CPRs of niobium NBJsof a cuboidal shape with a three-dimensional bank structure. Froma sine-wave to a sawtooth-like form, we showed that deviated CPRsof NBJs can be described quantitatively by its skewness & UDelta;& theta;.Furthermore, the measured dependence of & UDelta;& theta; on the criticalcurrent I (0) from 108 NBJs turned out tobe consistent with the calculated dependence derived from the changein geometric dimensions. This suggested that the CPRs of NBJs canbe tuned by their geometric dimensions. In addition, the calculatedscaling behavior of & UDelta;& theta; versus I (0) in 3D space was provided for the future designof superconducting circuits of a high integration level by using niobiumNBJs.