Superconductivity in non-centrosymmetric materials

• Superconductivity in absence of inversion symmetry of the crystal structure is characterised by a removal of the spin degeneracy of electrons which allows for spin-triplet pairing in the superconducting condensate, although a theorem of P.W. Anderson requires a centre of inversion in the crystal structure as an essential symmetry element for spin-triplet pairing.
• We show that unconventional superconductivity in such materials occurs only in those systems which exhibit strong correlations among electrons. If correlations are absent, simple s-wave superconductivity is observed in general.
• Here we present various members of this family of superconductors and discuss the ground state properties with respect to a number of microscopic and macroscopic experiments as well as in the context of ab initio electronic and phononic structure calculations.

Superconductivity in absence of inversion symmetry of the crystal structure is basically controlled by a Rashba-like antisymmetric spin orbit coupling which splits the Fermi surface and removes the spin degeneracy of electrons. The Fermi surface splitting can originate a mixing of spin-singlet and spin-triplet states in the superconducting condensate. The presence of spin-triplet states is expected to be responsible for various uncommon features of the superconducting ground state. Experimentally, distinct deviations from the expectations of the BCS theory are found, in general, only in those systems where beside the missing of inversion symmetry strong correlations among electrons are present. Materials of this group are primarily based on Ce, Yb or U. For the much larger group of materials without substantial electronic correlations, BCS-like superconductivity was observed in the overwhelming number of known examples. Hence, unconventional superconductivity requires, in general, the mutual presence of electronic correlations and non-centrosymmetric crystal structures.