Twisted multilayer nodal superconductors

Twisted bilayers of nodal superconductors were recently proposed as an attractive platform to host topological superconducting phases with spontaneously broken time reversal symmetry. Here we extend this analysis to twisted multilayers consisting of two high-symmetry stackings with (i) alternating or (ii) constant twist angles between successive layers. The alternating-twist stacking can be mapped, in analogy to alternating-twist multilayer graphene, to a collection of twisted bilayers with renormalized interlayer couplings, albeit with a remnant nodal d-wave order parameter when the number L of layers is odd. In contrast, the constant twist stacking exhibits physics beyond twisted bilayers, including the presence of band touchings with cubic dispersion when L = 3 (mod 4). Owing to their diverging density of states at the Fermi level, such cubic band touchings are susceptible to interaction-induced instabilities, which we explore using a self-consistent BCS mean-field theory.