  Within the framework of Ginzburg-Landau theory we study the rich variety of
interfacial phase transitions in twinning-plane superconductors. We show that
the phase behaviour strongly depends on the transparency of the twinning plane
for electrons measured by means of the coupling parameter \alpha_TP. By
analyzing the solutions of the Ginzburg-Landau equations in the limit of
perfectly transparent twinning planes, we predict a first-order interface
delocalization transition for all type-I materials. We further perform a
detailed study of the other limit in which the twinning plane is opaque. The
phase diagram proves to be very rich and fundamentally different from the
transparent case, recovering many of the results for a system with an external
surface. In particular both first-order and critical delocalization transitions
are found to be possible, accompanied by a first-order depinning transition. We
provide a comparison with experimental results and discuss the relevance of our
findings for type-II materials.
