Non-centrosymmetric superconductors

Superconductivity appears to be a macroscopic quantum phenomenon which relies on symmetries of the solid. In the simplest case, where two electrons form a Cooper pair with antisymmetric spins (i.e., s-wave, spin-singlet superconductivity), only gauge symmetry is broken. All materials, which belong to this symmetry type are termed conventional supercon-ductors. It is generally assumed that time reversal symmetry provides the necessary conditions for spin-singlet Cooper pairing, while spin-triplet pairing needs, in addition, inversion symmetry. The absence of a centre of inversion, i.e., a non-centrosymmetric (NCS) crystal structure, should thus be disadvantageous for forming a spin-triplet condensate. As parity is not conserved in NCS systems, pure spin singlets and spin triplets cannot be formed anymore.

Most of the known superconductors contain a centre of inversion in their crystal structures. Parity allows then to unambiguously discern between spin-singlet and spin-triplet pairs in the superconducting condensate. Besides, P. Anderson pointed out that spin-triplet pairing requires a centre of inversion in the crystal structure as an essential symmetry element. Time-reversal symmetry, on the other hand, provides the necessary conditions for spin-singlet Cooper pairing. The discovery of CePt3Si, as the first non-centrosymmetric (NCS) heavy fermion superconductor, revealed evidence of spin triplet Cooper pairs in the superconducting condensate. This finding against expectations triggered considerable research activities on such materials. The absence of inversion symmetry in a crystal structure gives rise to an electric field gradient parallel to the NCS crystal-axis. The resulting antisymmetric spin-orbit coupling (ASOC) subsequently lifts the two-fold spin degeneracy of the electronic bands. Electrons on these non-degenerate spin-split bands can then form Cooper pairs, either in the singlet or in the triplet channel. The mixing of Cooper pair channels is then a consequence of violated parity. CePt3Si exhibits strong correlations among electrons, as evidenced by a high Sommerfeld value of the specific heat. Such strong electron correlations might overlap the impact of the ASOC such that the initial driving force of unconventionality in systems like CePt3Si remains indistinguishable. Materials with strong electron correlations are characterized by a substantial value of the Coulomb correlation strength U, which can be of the order of several eV's. The lack of inversion symmetry leads to novel anomalous spin fluctuations, which stabilize the triplet part of the superconducting condensate, in addition to the singlet part, originating from centrosymmetric fluctuations. These anomalous fluctuations with anomalous momentum dependencies vanish in centrosymmetric systems, but become enhanced by onsite Coulomb correlations. Within this scenario, absence of correlations brings about the absence of anomalous fluctuations and thus, spin-triplet pairing should no longer occur in a simple NCS system. Studies in the context of the FWF P2295 on materials without strong correlations among electrons revealed that the superconducting ground state can be accounted for in terms of singlet pairing (s-wave) of electrons and many of the physical properties follow the prediction of the BCS theory. The split Fermi surfaces due to ASOC, which can be tuned by changing appropriately the constituting elements of the system, however, provides a few rare sites, where spin-triplet pairing is possible. Studies by muon-spin rotation allowed to conclude that time reversal symmetry breaking is not an inherent property of superconductors without inversion symmetry. This was shown for BaPtSi3 and Mo3Al2C, NCS superconductors introduced by the project leaders. Altogether, about 10 new superconductors have been found and characterized in terms of the research project FWF P22295.