Josephson interferometer in a ring topology as a symmetry prove of Sr₂RuO₄

The Josephson effect is theoretically studied in two types of SQUIDs consisting of $s$ wave superconductor and Sr$_2$RuO$_4$. Results show various response of the critical Josephson current to applied magnetic fields depending on the type of SQUID and on the pairing symmetries. In the case of a $p_x+ip_y$ wave symmetry, the critical current in a corner SQUID becomes an asymmetric function of magnetic fields near the critical temperatures. Our results well explain a recent experimental finding [Nelson et. al, Science \textbf{306}, 1151 (2004)]. We also discuss effects of chiral domains on the critical current.