Gradient energy of superconductors without inversion symmetry

•We find novel gradient terms in the free energy of noncentrosymmetric superconductors.•Nonuniform superconducting states might be possible even in the absence of any external fields.•Noncentrosymmetric superconductors can support phase solitons.

We show that the Ginzburg–Landau free energy of a noncentrosymmetric superconductor contains an unusual term which is linear in spatial gradients (the Lifshitz invariant). This can result, in a certain range of parameters, in the superconducting state being nonuniform, even in the absence of a magnetic field. The microscopic origin of the Lifshitz invariant can be traced to the dependence of the pairing interaction on the center-of-mass momentum of the Cooper pairs.