Fig. 1-8 Schematic diagram of the wave functions and spin direction of two electrons constituting a Cooper pair xi denotes a measure of the extent of the wave function. (a) s-wave : The orbital angular momentum is 0 and the electron distribution is symmetric. The spin directions of the two electrons are opposite, which corresponds to the case represented by the standard BCS theory. (b) d-wave : The orbital angular momentum is 2, i.e., the wave function is symmetric against the exchange of the position of the two electrons (even parity). (c) p-wave : The orbital angular momentum is 1, i.e., the wave function is anti-symmetric against the exchange of the positions of the two electrons (odd parity).

The mechanism of standard (low-temperature) superconductivity is successfully explained by the Bardeen-Cooper-Schrieffer (BCS) theory. According to this theory, as a result of the formation of Cooper pairs, all of the paired electrons are condensed into the ground state, and are separated from the excited state by a uniform energy gap. The paired electrons then flow freely without resistivity and the superconducting state appears. Though a quantum state can normally only be occupied by a single particle with spin 1/2, the spin of a Cooper pair consisting of two electrons is an integer (0 or 1) so the condensation is realizable. For high temperature superconductors, the mechanisms of the superconductivity such as the formation process of the Cooper pairs and the way the material features are determined have not been understood completely. A Uranium compound UPt3 is a peculiar superconducting material which has two transition temperatures near 0.5 K and three superconducting phases, A, B, and C. This peculiarity comes from the anisotropy of the above-described energy gap between the ground state of the condensed particles and the excited state. From this fact it is already well known that the Cooper pairs can not consist of two electrons in the s-wave state (where one electron is distributed spherically symmetrically around the other). In spite of intensive worldwide research, however, it had not previously been determined whether or not the spins of the two electrons of the Cooper pair are in the same direction, and therefore, whether it has an orbital angular momentum such that the sign of the wave-function is invariant with the interchange of the two electrons (even parity, d-wave etc.) or not (odd parity, p-wave etc.). We successfully showed that the directions of the two spins are the same, by growing a high quality single crystal of UPt3 and performing NMR measurements of the spin magnetization due to the external magnetic field. This result demonstrates for the first time that UPt3 is an odd-parity superconducting material (Fig. 1-8).

Reference H. Tou et al., Odd-parity Superconductivity with Parallel Spin Pairing in UPt3 : Evidence from 195Pt Knight Shift Study, Phys. Rev. Lett., 77, 1374 (1996).

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