  Superconducting materials with noncentrosymmetric lattices lacking space
inversion symmetry exhibit a variety of interesting parity-breaking phenomena,
including the magneto-electric effect, spin-polarized currents, helical states,
and the unusual Josephson effect. We demonstrate, within a Ginzburg-Landau
framework describing noncentrosymmetric superconductors with $O$ point group
symmetry, that vortices can exhibit an inversion of the magnetic field at a
certain distance from the vortex core. In stark contrast to conventional
superconducting vortices, the magnetic-field reversal in the parity-broken
superconductor leads to non-monotonic intervortex forces, and, as a
consequence, to the exotic properties of the vortex matter such as the
formation of vortex bound states, vortex clusters, and the appearance of
metastable vortex/anti-vortex bound states.
