This picture.(53.6KB)

Fig. 7-6 Schematic views of electron pair wave functions, and a phase diagram of a theoretical model on a honeycomb lattice (a) Various kinds of electron pair wave-functions are illustrated. The BCS theory envisions spin-singlet s-wave pairing mediated by the electron-lattice interaction. In high-Tc cuprates, spin-singlet d-wave pairing is realized in order to avoid the effects of Coulomb repulsion. For the case of spin triplet pairing, there occurs a p-wave state with odd-parity under space inversion. (b) Phase diagram obtained by analyzing a theoretical model on a honeycomb lattice. An unphysical region is shown in gray. In the ferromagnetic state, a superconducting phase with odd-parity triplet pairing occurs. The unit cell of the honeycomb lattice contains two atomic sites, 1 and 2. As denoted by a cross, an inversion center is located just midway between the two sites. In such a case, local triplets due to the Hund's rule interaction can form bonding and anti-bonding states inside the unit cell, leading to even and odd-parity triplet pairing states, respectively.

Superconductivity is quantum-mechanical phenomenon occurring on a macroscopic scale. The occurrence of such a phenomenon indicates the condensation of a macroscopic number of electrons into the same quantum state. The mechanism of such condensation of fermionic electrons into the same state while satisfying the Pauli principle has been explained by the famous BCS theory in 1957. An important point of this theory is the condensation of a macroscopic number of bosons composed of pairs of electrons with opposite spin directions into the same momentum state. In general, there is a large Coulomb repulsion between electrons, but due to an effective attraction mediated by lattice vibrations, it is possible to form electron pairs. In the BCS theory, an s-wave pair mediated by lattice vibrations has been assumed, as shown in Fig. 7-6 (a). In high-Tc cuprates, d-wave pairs mediated by spin fluctuations, not by lattice vibrations, has been suggested. In any case, pairs have always been composed of two electrons with opposite spin directions. However, in ruthenates and certain uranium (U) compounds, it has recently been revealed experimentally that electrons with the same direction of spin can form triplet pairs. In this case, the pairing wave function is a p-wave with odd-parity for space inversion. Concerning the origin of spin triplet pairing, one can consider the Hund's rule interaction, which causes the spin directions of electrons occupying different orbitals to align, forming a local spin triplet. However, we cannot explain the odd-parity, since the local triplet pair must have a finite amplitude on an atomic site. Then, we have analyzed a theoretical model with orbital degrees of freedom on several types of lattice. As shown in Fig. 7-6 (b), for a non-Bravais lattice such as a honeycomb lattice, in which the inversion center is not located at an atomic site, local triplets due to the Hund's rule interaction can form anti-bonding states inside the unit cell, leading to odd-parity triplet pairing. Spin triplet pairing has also been proposed for U compounds such as UPt3 and UGe2. We envision a possible application of the present scenario to these materials as well, since the crystal structure is classified as a non-Bravais lattice.

Reference T. Hotta et al., Odd-Parity Triplet Pair Induced by Hund's Rule Coupling, Phys. Rev. Lett., 92(10), 107007 (2004).

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