Topological Phase Transitions in 2.5 D Twisted Nodal Superconductors

Under the application of an interlayer supercurrent, twisted bilayers of nodal superconductors have been predicted to host topological states. Experiments on cuprate materials, however, are so far limited to finite thickness flakes containing many layers, raising the question how topological effects may be altered. We demonstrate that in finite-thickness flakes experimental signatures of topological superconductivity remain robust and new topological transitions arise, that have no analogue in bilayers. 

We study an N layered flake of d_x²-y² superconductor with only one (top) layer twisted with respect to the others, and a c-axis supercurrent through the system. For a weak current, the low-energy quasiparticle dispersion contains 4N gapped Dirac nodes with a total Chern number of |C| = 2N. The average gap size decreases as O(1/N), but at large twist angles the gap of the top layer remains robust to increasing N, making this regime promising for scanning tunneling microscopy experiments. Increasing the current leads to a sequence of topological transitions, eventually increasing the Chern number to be of the order O(N²). We discuss the signatures of these transitions in thermal Hall effect, demonstrating that it is robust to increasing layer thickness at intermediate temperatures.