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.