First-principles study of the noncentrosymmetric superconductors Li$_2$Pt$_3$B and Li$_2$Pd$_3$B

Effect of spin-orbit coupling (SOC) associated with lack of space-inversion symmetry has been a central issue in condensed-matter physics. Li$_2$Pt$_3$B and Li$_2$Pd$_3$B are superconducting below 2.7 K and 7 K, respectively, and have the same crystal structure (cubic $P4_3 32$, No.~212), which is noncentrosymmetric and is characterized by highly distorted corner-sharing BPt(Pd)$_6$ octahedra. Despite the same valency and structure, they show quite different superconducting behavior. NMR measurements [1] indicate that Li$_2$Pt$_3$B would be a spin-triplet superconductor with line nodes in the gap function while Li$_2$Pd$_3$B is a conventional spin-singlet $s$-wave superconductor. SOC would be a key to understand this difference. To clarify the electronic band structure and Fermi surface of these compounds, we performed density-functional (GGA PBE) calculations with FLAPW method. Relativistic effects were fully taken into account. The band structures calculated are in good accordance with previous work[2] and the spin splitting due to SOC is quite significant in Li$_2$Pt$_3$B. This work was supported by a MEXT KAKENHI on Innovative Areas ``Topological Quantum Phenomen''. [1] M.~Nishiyama, Y.~Inada, and G.-q.~Zheng, PRL {\bf 98}, 047002 (2007); PRB {\bf 71}, 220505(R) (2005). [2] K.-W.~Lee and W.~E.~Pickett, PRB {\bf 72}, 174505 (2005).