3.1.1 Magnetic field dependence

Measurements by Delsing et al⁹ on similar arrays have shown that for low magnetic field, V_t varies periodically with the field. At higher fields (25-40 mT) V_t increases and then decreases to the normal state V_t. The measurements in this report were all made at fields less than 5 mT and only the periodic behavior was observed, with a period of 1.62 mT. This period corresponds to a frustration of 1. Frustration is defined as f=BA/₀, where A is the area of one unit cell in the tunnel junction array and ₀=h/2e is the magnetic flux quantum. A unit cell is the total area of the array divided by the number of loops. The unit cell is independent of the London penetration depth, because the magnetic flux expelled from the islands in a 2D-array does not leave the array, but is collected in the loops. The effective unit cell area thus becomes the area of one loop plus the area of one island. Taking the area in the SEM picture (figure 2b), A=1.3 µm², the expected period B/f=₀/A=1.6 mT is in excellent agreement with the measured period. The difference between high and low Vt is about 0.1 mV, which is easily measurable. Figure 7 shows several I-V curves taken at frustrations from -1.2 to 0.5. They are measured in R-bias mode and therefore there is no current jump in the graph. The curves are very noisy below 1 nA because the current actually switches rapidly between two points on the loadline determined by the two current measurement resistors. In V-bias mode there is no switching and all V_t measurements were made in V-bias mode.

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