The determination of the supercurrent-phase relation of superconducting weak links in static condition

Abstract

Two methods are developed for the determination of the supercurrent-phase relation of a weak link over the complete phase range. The weak link is incorporated in a superconducting ring, a so-called SQUID ring, which is constructed in such a way that on either side of the weak link an external supercurrent is inserted. With constant applied magnetic field a circulating supercurrent is induced in the SQUID ring. In the first method an external supercurrent is inserted with such a polarity and size that the difference between the embraced magnetic flux and the applied flux is zeroed. This is accomplished with the help of a commercial flux SQUID detector. The circuit is then balanced; the circulating current is zeroed and the inserted supercurrent flows entirely through the junction. The corresponding phase difference over the junction is determined by the amount of applied flux. In the second method the detected embraced magnetic flux signal is traced as a function of the applied flux in case of zero and finite external supercurrent. It is argued that the two curves which can be obtained in this way can be mapped on each other by a horizontal and a vertical displacement. The horizontal displacement gives the self-inductance of the SQUID ring and the vertical displacement gives the amplification factor so that the complete supercurrent-phase relation can be determined directly. In both methods the self-inductance is less than ( h ̵ 2ei c ) so that flux jumps in the loop do not occur ( i c is the critical current of the weak link). Deviations from a pure sinusoidal supercurrent-phase relation are observed in a s-s'-s Josephson junction.