Most superconducting materials have an inversion center in their crystal lattices. One of few exceptions is the recently discovered heavy-fermion superconductor ${\mathrm{CePt}}_3\mathrm{Si}$ [E. Bauer et al., Phys. Rev. Lett. 92, 027003 (2004)]. In this paper, we analyze the implications of the lack of inversion symmetry for the superconducting pairing. We show that the order parameter is an odd function of momentum, and that there always are lines of zeros in the excitation energy gap for one-component order parameters, which seems to agree with the experimental data. The superconducting phase can be nonuniform, even without external magnetic field, due to the presence of unusual gradient terms in the Ginzburg-Landau free energy. Also, we performed ab initio electronic structure calculations for ${\mathrm{CePt}}_3\mathrm{Si},$ which showed that the spin-orbit coupling in this material is strong, and the degeneracy of the bands is lifted everywhere except along some high symmetry lines in the Brillouin zone.

• Received 11 November 2003

DOI:https://doi.org/10.1103/PhysRevB.69.094514