  Stabilizing superconductivity at high temperatures and elucidating its
mechanism have long been major challenges of materials research in condensed
matter physics. Meanwhile, recent progress in nanostructuring offers
unprecedented possibilities for designing novel functionalities. Above all,
thin films of cuprate and iron-based high-temperature superconductors exhibit
remarkably better superconducting characteristics (e.g. higher critical
temperatures) than in the bulk, but the underlying mechanism is still not
understood. Solving microscopic models suitable for cuprates, here, we
demonstrate that at an interface between a Mott insulator and an overdoped
non-superconducting metal, the superconducting amplitude stays always pinned at
the optimum achieved in the bulk, independently of the carrier concentration in
the metal. This is in contrast to the dome-like dependence in bulk
superconductors, but consistent with the astonishing independence of the
critical temperature from the carrier density x observed at interfaces of
La2CuO4 and La2-xSrxCuO4. We furthermore identify a self-organization mechanism
as responsible for the pinning at the optimum amplitude: An emergent electronic
structure induced by interlayer phase separation eludes bulk phase separation
and inhomogeneities that would kill superconductivity in the bulk. Thus,
interfaces provide an ideal tool to enhance and stabilize superconductivity.
This interfacial example opens up further ways of shaping superconductivity by
suppressing competing instabilities, with direct perspectives for designing
devices.
