Sommerfeld Theory Colloquium, To pinpoint the microscopic mechanism for superconductivity has

proven to be one of the most outstanding challenges in the physics of

correlated quantum matter. Thus far, the most direct evidence for

an electronic pairing mechanism is the observation of a new symmetry

of the order-parameter, as done in the cuprate high-temperature

superconductors. Like distinctions based on the symmetry of a locally

defi�ned order-parameter, global, topological invariants allow for

a sharp discrimination between states of matter that cannot be transformed

into each other adiabatically. Here we propose an unconventional

pairing state for the electron

uid in two-dimensional oxide

interfaces and establish a direct link to the emergence of nontrivial

topological invariants. Topological superconductivity and Majorana edge states can then be used to detect the microscopic origin for

superconductivity. In addition, we show that also the density wave

states that compete with superconductivity sensitively depend on the

nature of the pairing interaction. Our conclusion is based on the special

role played by the spin-orbit coupling and the shape of the Fermi

surface in SrTiO3/LaAlO3-interfaces and closely related systems.