Impurity and vortex states in the bilayer high-temperature superconductor La3Ni2O7

We perform a theoretical examination of the local electronic structure in the recently discovered bilayer high-temperature superconductor ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$. Our method begins with a bilayer two-orbital tight-binding model, incorporating various pairing interaction channels. We determine superconducting order parameters by self-consistently solving the real-space Bogoliubov--de Gennes (BdG) equations, revealing a robust and stable extended $s$-wave pairing symmetry. We investigate the single impurity effect using both self-consistent BdG equations and non-self-consistent $T$-matrix methods, uncovering low-energy in-gap states that can be explained with the $T$-matrix approach. Additionally, we analyze magnetic vortex states using a self-consistent BdG technique, which shows a peak-hump structure in the local density of states at the vortex center. Our results provide identifiable features that can be used to determine the pairing symmetry of the superconducting ${\mathrm{La}}_{3}{\mathrm{Ni}}_{2}{\mathrm{O}}_{7}$ material.