Impurity effects on local electronic structure of twisted bilayer cuprates

It has been recently proposed that a fully gapped $d$-wave superconducting phase emerges in twisted bilayer cuprates when twist angle is in the vicinity of ${45}^{\ensuremath{\circ}}$. By considering a twisted bilayer model with a moir\'e cell, we study the local electronic structure around a single-site impurity and impurity dimer in both topologically trivial and nontrivial superconducting states. We find that the topological nontrivial superconducting phase is robust against single scalar-potential impurity scattering but is very sensitive to the interlayer impurity dimer scattering, which avoids and enforces the creation of the subgap quasiparticle state. This behavior is intrinsic to the bilayer structure and topological nature, in contrast to the other types of impurities that inevitably bring subgap quasiparticle states. We expect that our results can contribute to the understanding of electronic properties of twisted bilayer cuprates systems.