Adatom Engineering Magnetic Order in Superconductors: Applications to Altermagnetic Superconductivity.

We study theoretically how superlattices based on adatoms on surfaces of unconventional superconductors can be used to engineer novel pairing states that break time-reversal symmetry and exhibit nontrivial magnetic point symmetries. We illustrate this using a square-lattice Hubbard model with d-wave superconductivity and a subleading s-wave state as an example. An adatom superlattice with square-lattice symmetries is shown to stabilize an "orbital altermagnetic superconductor," a state that exhibits loop current patterns and associated orbital magnetic moments, which preserve superlattice translations but are odd under fourfold rotations. This state is further characterized by a nonzero Berry curvature quadrupole moment and, upon including spin-orbit coupling, by an altermagnetic spin splitting of the bands and nontrivial spin textures in the superlattice unit cell, with zero net spin moment.