Mixed pairing state in Ru microdomains embedded in bulk single-crystal Sr$_2$RuO$_4$

We performed detailed tunneling measurements on Ru microdomains embedded in Sr$_2$RuO$_4$ using In-Ru/Sr$_2$RuO$_4$ junctions prepared by pressing freshly cut pure In wire onto a cleaved $ab$ face of a Ru-containing Sr$_2$RuO$_4$ single crystal. We observed a superconducting transition temperature of 0.45 K and a $T$ = 0 superconducting energy gap of 0.10 meV that are associated with the Ru microdomains. The systematic behavior observed in the tunneling spectra, including the presence of a Josephson coupling between In and Ru, a zero bias conductance peak (ZBCP), an unusually large magnitude and the temperature and magnetic field dependences of the superconducting energy gap, suggests that both $s$- and $p$-wave pairings are present simultaneously in the interior of a Ru microdomain. We propose the existence of a novel superconducting state featuring the mixing of the $s$- and the $p$-wave pairings in this unique superconducting system and discuss the properties of this mixed pairing state.