Effect of charging energy on critical current of dc-SQUID comprising two sub-micron aluminum Josephson junctions

Highlights: ► We measure the capacitance of Al Josephson junctions by using the dc-SQUID methods. ► Both the Josephson coupling energy and charging energy in the SQUID are evaluated. ► The interference pattern is found to be deviated from the classical theory. ► The deviation is enhanced by decreasing the Josephson coupling energy. ► Our model including the quantum phase fluctuation can explain the deviation. -- Abstract: Tiny Al/AlOx/Al tunnel junctions are widely used in single-electron, single-Cooper-pair, and quantum-bit devices. A crucial parameter for such devices is the charging energy of a single electron or a single Cooper-pair in the junctions, and hence, determination of the junction capacitance is quite important. In this paper, we report our experiments to determine the capacitance of sub-micron Al tunnel junctions. We employ a SQUID resonance technique. Differently from the work reported by Deppe et al. [4], the loop inductance is obtained by not only numerical calculation but also experimental results of quantum interference, which eliminates uncertainty about the field penetration depth of Al thin films. The specific capacitance is obtained as 54 fF/μm2. We have also found that the critical current of the dc-SQUID is smaller than the value given by the classical theory for large Josephson junctions. Calculation including the charging energy effect provides better fitting to the experiments, where the critical current is assumed to be proportional to the square root of the ratio of the Josephson coupling energy to the charging energy