Impurity and vortex States in the bilayer high-temperature superconductor $\mathrm{La}_3\mathrm{Ni}_2\mathrm{O}_7$

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.