  In noncentrosymmetric crystals, nonuniform superconducting states are
possible even in the absence of any external magnetic field. The origin of
these states can be traced to the Lifshitz invariants in the free energy, which
are linear in spatial gradients. We show how various types of the Lifshitz
invariants in noncentrosymmetric superconductors can be derived from
microscopic theory.

Superconductivity