  Domains in non-centrosymmetric materials represent regions of different
crystal structure and spin-orbit coupling. Twin boundaries separating such
domains display unusual properties in non-centrosymmetric superconductors
(NCS), where magneto-electric effects influence the local lower and upper
critical magnetic fields. As a model system, we investigate NCS with tetragonal
crystal structure and Rashba spin-orbit coupling (RSOC), and with twin
boundaries parallel to their basal planes. There, we report that there are two
types of such twin boundaries which separate domains of opposite RSOC. In a
magnetic field parallel to the basal plane, magneto-electric coupling between
the spin polarization and supercurrents induces an effective magnetic field at
these twin boundaries. We show this leads to unusual effects in such
superconductors, and in particular to the modification of the upper and lower
critical fields, in ways that depend on the type of twin boundary, as analyzed
in detail, both analytically and numerically. Experimental implications of
these effects are discussed.
