2.5-dimensional topological superconductivity in twisted superconducting flakes

Multilayer flakes of two-dimensional materials were recently shown to be tunable by twisting monolayers on their surface. This raises the question whether qualitatively new phenomena can occur in such finite-thickness moiré systems. Here we demonstrate the emergence of distinct topological phases and transitions in N-layered flakes of nodal superconductors with a single monolayer twisted on top of it. We show that a c-axis current transforms the whole system into a chiral topological superconductor. Increasing the current drives a sequence of topological transitions between states characterized by a Chern number increasing from $$\sim {\mathcal{O}}(N)$$ up to $$\sim {\mathcal{O}}({N}^{2})$$ , well beyond the additive effect of stacking N layers. We predict thickness-independent signatures of these states in the thermal Hall and tunneling microscopy measurements. Twisted superconductor flakes thus provide an example of a “2.5-dimensional” material where the synergy of two-dimensional layers extended in a third dimension realize states inaccessible in either monolayer or bulk materials.