Three “universal” mesoscopic Josephson effects

A recent theory is reviewed for the sample-to-sample fluctuations in the critical current of a Josephson junction consisting of a disordered point contact or microbridge. The theory is based on a relation between the supercurrent and the scattering matrix in the normal state. The root-mean-square amplitude rms Ic of the critical current Ic at zero temperature is given by rms Ic ≃ e∆0/h̄, up to a numerical coefficient of order unity (∆0 is the energy gap). This is the superconducting analogue of “Universal Conductance Fluctuations” in the normal state. The theory can also be applied to a ballistic point contact, where it yields the analogue of the quantized conductance, and to a quantum dot, where it describes supercurrent resonances. All three phenomena provide a measurement of the supercurrent unit e∆0/h̄, and are “universal” through the absence of a dependence on junction parameters.