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We perform a theoretical examination of the local electronic structure in therecently discovered bilayer high-temperature superconductor${\mathrm{La}_3\mathrm{Ni}_2\mathrm{O}_7}$. Our method begins with a bilayertwo-orbital tight-binding model, incorporating various pairing interactionchannels. We determine superconducting order parameters by self-consistentlysolving the real-space Bogoliubov-de Gennes (BdG) equations, revealing a robustand stable extended s-wave pairing symmetry. We investigate the single impurityeffect using both self-consistent BdG equations and non-self-consistentT-matrix methods, uncovering low-energy in-gap states that can be explainedwith the T-matrix approach. Additionally, we analyze magnetic vortex statesusing a self-consistent BdG technique, which shows a peak-hump structure in thelocal density of states at the vortex center. Our results provide identifiablefeatures that can be used to determine the pairing symmetry of thesuperconducting ${\mathrm{La}_3\mathrm{Ni}_2\mathrm{O}_7}$ material.

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