Study of an array of superfluid ³He weak links

An array of 1126 identical microapertures is used as the hydrodynamic inductance in a superfluid ³He Helmholtz resonator. Each aperture is 0.27 micron square, fabricated by e-beam lithography in a 0.1 micron thick SiN membrane. These dimensions are not too much larger than the superfluid coherence length and therefore, particularly at higher temperatures, an aperture might be thought of as a Josephson weak link (in the sense of a Dayem bridge). The superfluid ³He critical mass current, I_c, through this array has been measured over a wide range of temperatures. The results indicate that the critical current has a Ginzburg-Landau form of I_c=l_co(1-T/T_c) ^3/2. This temperature dependence is consistent with phase slippage (not necessarily involving vortices), at the pair breaking velocity, as the critical mechanism.