Recent Developments in the Studies of Sr$_{2}$RuO$_{4}$: Suppression of the Upper Critical Field and the Interference between the Even-Parity Superconductivity and the Superconductivity of Sr$_{2}$RuO$_{4}$

Although there are a number of convincing experimental evidence for odd-parity, spin-triplet superconductivity of Sr$_{2}$RuO$_{4}$, there are still a few puzzling phenomena not yet clarified in this framework. To describe recent progress, we mainly present on the accurate and precise dependence of the upper critical field $H_{c2}$ on the field direction and temperature. Compared with the extension of the initial slope of $H_{c2}$ vs.$ T$ near $T_{c}$, the low-temperature $H_{c2}$ is strongly suppressed only when the field direction is within a few degrees form the exact in-plane direction. Interestingly, if the anisotropic ratio in Sr$_{2}$RuO$_{4}$ is assumed to depend on temperature, the observed angular dependence of $H_{c2}$ is reproduced better at lower temperature with an effective-mass model for an anisotropic three-dimensional superconductor. The magnitude of the suppression is rather comparable to that known for UPt$_{3}$, another strong candidate of the odd-parity superconductor. Concerning another development, we will present on the unusual temperature dependence of the critical current between the so-called 3-K phase (a eutectic crystal of Sr$_{2}$RuO$_{4}$ with Ru-metal inclusions) and lead deposited on the surface of the 3-K phase crystal. The critical current of such proximity junctions exhibits extraordinary dependence, dropping sharply below $T_{c}$ = 1.5 K of Sr$_{2}$RuO$_{4}$, but abruptly starting to increase again below about 1.1 K. Such behavior is most naturally ascribable as an interference between the even-parity and odd-parity superconductivity..