Vortical versus skyrmionic states in the topological phase of a twisted bilayer with <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>d</mml:mi></mml:math>-wave superconducting pairing

It was recently shown that a chiral topological phase emerges from the coupling of two twisted monolayers of superconducting ${\mathrm{Bi}}_{2}{\mathrm{Sr}}_{2}{\mathrm{CaCu}}_{2}{\mathrm{O}}_{8+\ensuremath{\delta}}$ for certain twist angles. In this work, we reveal the behavior of such twisted superconducting bilayers with ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ 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.