Vortical versus skyrmionic states in the topological phase of a twisted bilayer with d -wave superconducting pairing

It was recently shown that a chiral topological phase emerges from the coupling of two twisted monolayers of superconducting Bi₂Sr₂CaCu₂O_8+δ for certain twist angles. In this work, we reveal the behavior of such twisted superconducting bilayers with d_x²-y² pairing symmetry in the presence of an applied magnetic field. Specifically, we show that the emergent vortex matter can serve as a smoking gun for the detection of topological superconductivity in such bilayers. Moreover, we report two distinct skyrmionic states that characterize the chiral topological phase and provide a full account of their experimental signatures and their evolution with the twist angle.