The nanobridge junction (NBJ) is a type of Josephson junction that is advantageous for the miniaturization of superconducting circuits. However, the current-phase relation (CPR) of the NBJ usually deviates from a sinusoidal function, which has been explained by a simplified model with correlation only to its effective length. Here, we investigated both measured and calculated CPRs of niobium NBJs of a cuboidal shape with a three-dimensional bank structure. From a sine-wave to a sawtooth-like form, we showed that deviated CPRs of NBJs can be described quantitatively by its skewness Δθ. Furthermore, the measured dependence of Δθ on the critical current I0 from 108 NBJs turned out to be consistent with the calculated dependence derived from the change in geometric dimensions. This suggested that the CPRs of NBJs can be tuned by their geometric dimensions. In addition, the calculated scaling behavior of Δθ versus I0 in 3D space was provided for the future design of superconducting circuits of a high integration level by using niobium NBJs.
Keywords: Josephson effect; current−phase relation; geometric scaling; nanobridge junction; superconducting circuit.