Interference-controlled magnetic bound states and subgap transport in a Square--octagon superconductor

Abstract

The square--octagon lattice provides a useful setting for studying magnetic adatoms because its multisublattice structure allows different adsorption geometries to probe distinct combinations of the host electronic states. We study magnetic adatoms in an $s$-wave superconducting square--octagon lattice, focusing on the interplay between adsorption geometry, narrow and flat-band states, and subgap transport. We find that the large spectral weight associated with a flat band does not necessarily imply strong impurity--host coupling. For symmetric square-hollow adsorption, destructive interference strongly suppresses the overlap with the flat-band manifold, whereas top and octagon-hollow adsorption retain substantial overlap. This selectivity is reflected in the magnetic bound states, with the square-hollow channel supporting a predominantly atomic state, while the top and octagon-hollow states are strongly hybridized with the superconducting host. The effect develops continuously as the relevant band becomes flatter and remains pronounced in a material-motivated parameter regime. In a normal--superconductor--normal geometry, these differences are also reflected in the nonlocal subgap conductance. At a representative exchange splitting, square-hollow adsorption suppresses the low-bias conductance relative to the clean device, whereas octagon-hollow adsorption enhances it, with the square-hollow response showing a much sharper dependence on exchange splitting. Our results show that the magnetic-adatom response in narrow and flat-band superconductors is governed by the available spectral weight and by the symmetry and wave-function structure of the impurity--host hybridization.