Design principles for time-reversal symmetry breaking superconductivity in interfaces and two-dimensional sheets

By combining symmetry and energetic arguments, we show that, in any two-dimensional system with non-degenerate Fermi surfaces, a three-fold rotation symmetry of the high-temperature phase is a necessary condition for having a Cooper instability that spontaneously breaks time-reversal symmetry. Applying this result to the oxide heterostructures, we conclude that the observed superconductivity at the $[001]$ and $[110]$ interfaces is expected to be invariant under time-reversal. On a more general level, our considerations might serve as a design principle in the search for time-reversal symmetry breaking topological superconductivity in the absence of external magnetic fields.