  We study theoretically a model for twin boundaries in superconductors with
Rashba spin-orbit coupling, which can be relevant to both three-dimensional
noncentrosymmetric tetragonal crystals and two-dimensional gated
superconductors such as the LaAlO$_3$/SrTiO$_3$ interface. In both cases, the
broken inversion symmetry allows for a coexistence of singlet and triplet
pairing. Within the framework of a Ginzburg-Landau theory, we identify two
$\mathbb{Z}_2$ symmetries that are broken via two consecutive second order
phase transitions as the temperature is lowered. We show that a time-reversal
symmetry breaking superconducting state nucleates near the twin boundary if
singlet and triplet pairing amplitudes are of comparable magnitude. As a
consequence, the tendency towards ferromagnetic order is locally increased
along with the emergence of spontaneous supercurrents parallel to the twin
boundary. Spin currents, which are present in the form of Andreev bound states,
are found enhanced in the time-reversal broken phases.
