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The nano-bridge junction (NBJ) is a type of Josephson junction that isadvantageous for the miniaturization of superconducting circuits. However, thecurrent-phase relation (CPR) of the NBJ usually deviates from a sinusoidalfunction which has been explained by a simplified model with correlation onlyto its effective length. Here, we investigated both measured and calculatedCPRs of niobium NBJs of a cuboidal shape with a three-dimensional bankstructure. From a sine-wave to a saw-tooth-like form, we showed that deviatedCPRs of NBJs can be described quantitatively by its skewness {\Delta}{\theta}.Furthermore, the measured dependency of {\Delta}{\theta} on the criticalcurrent {I_0} from 108 NBJs turned out to be consistent with the calculatedones derived from the change in geometric dimensions. It suggested that theCPRs of NBJs can be tuned by their geometric dimensions. In addition, thecalculated scaling behavior of {\Delta}{\theta} versus {I_0} inthree-dimensional space was provided for the future design of superconductingcircuits of a high integration level by using niobium NBJs.

Geometric Scaling of the Current-Phase Relation of Niobium Nano-Bridge Junctions