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Ginzburg-Landau description of twin boundaries in noncentrosymmetric superconductors

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.