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Figure 3. Two close-up SEM pictures of a 2D-array. (a) The Hall probes are connected through three tunnel junctions to the array. The bright areas are isolated aluminum islands that get charged by the SEM. (b) The connecting bar at the top of the array. Note that the topmost loops are physically the same size as the rest of the loops. However, because the London penetration depth is of the order of the island dimensions, and the flux expelled from the bar is collected by the topmost loops, the effective loop size is actually larger, giving rise to a shorter period in magnetic field.

2.3 Measurement techniques

The measurements were carried out in a dilution refrigerator which was situated in an electrically shielded room. All digital equipment was situated outside of this room, and the digital ground was separated from the measurement ground with isolation transformers. The signals were amplified in an amplifier box located on top of the cryostat in order to minimize external pickup in the leads. The voltage across the sample was applied in one of to ways: in R-bias mode, the DC voltage was applied over two current measurement resistors in series with the sample; in V-bias mode the DC voltage over the sample was fixed by regulating the voltage with a feedback circuit.

The threshold voltage measurements were carried out using a sample-and-hold circuit specifically built for this purpose. This circuit would detect the moment when the current jumped from zero to a finite value. At that moment it would sample and hold the input voltage, giving a constant voltage to a voltmeter and sending a trig pulse to the same voltmeter. The voltage over the sample was ramped from a starting value, Vs, to 860 µV. The voltage ramp was generated by a function generator, and the frequency was varied between 2.4 Hz to 76.8 Hz (see figure 4). One Vt measurement was made in every period.


Figure 4. The voltage ramps used for the threshold voltage measurements.


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