3.2 Zero-bias resistance

A number of I vs. V_x and V_y measurements were taken on sample H9#44, at different magnetic fields. The current, I, ran from the top to the bottom bar, the normal voltage, V_x, was measured between the same bars and the Hall voltage, V_y, was measured between the two middle Hall probes (see figure 2a). This sample showed no threshold voltage, but an applied magnetic field affected the IV curves in a periodic manner. By measuring the slope of an I-V_x curve at almost zero current the zero-bias resistance, R₀, can be calculated. The result is displayed in figure 14, which shows R₀ vs. frustration, where frustration 1 corresponds to magnetic field strength 1.62 mT. The resistance goes down to zero at integer frustrations and decreases at rational frustrations, 1/2, 1/3, 2/3 and so on. This is in agreement with previous measurements by van der Zant et al⁷ and Chen et al⁶.

There are a few extra peaks in figure 14, at frustrations -0.88, -0.31, 0.26 and 0.84. They have a period of about 0.57 frustration units. Note that the threshold voltage measurements on chip H7#43 showed similar peaks at the same frustrations (see figure 8). The explanation has most likely to do with loops with bigger effective area than A, which would give shorter periods. At the solid bars at the top and bottom of the array are some loops with the same physical area as the loops inside the array (see figure 2b). However, those loops will collect some of the magnetic field that is expelled from the bars (Meissner effect), increasing the effective area. The London penetration depth may be bigger in the bars than in the Al islands, increasing the effective area even more. Similar phenomena has been observed in one-dimensional arrays of SQUIDs by Haviland¹¹.

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