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Interplay of Magnetism and Topological Superconductivity in Bilayer Kagome Metals

The binary intermetallic materials, $M_3$Sn$_2$ ($M$ = 3d transition metal) present a new class of strongly correlated systems that naturally allows for the interplay of magnetism and metallicity. Using first principles calculations we confirm that bulk Fe$_3$Sn$_2$ is a ferromagnetic metal, and show that $M$ = Ni and Cu are paramagnetic metals with non-trivial band structures. Focusing on Fe$_3$Sn$_2$ to understand the effect of enhanced correlations in an experimentally relevant atomistically thin single kagome-bilayer, our ab-initio results show that dimensional confinement naturally exposes the flatness of band structure associated with the bilayer kagome geometry in a resultant ferromagnetic Chern metal. We use a multistage minimal modeling of the magnetic bands progressively closer to the Fermi energy. This effectively captures the physics of the Chern metal with a non-zero anomalous Hall response over a material relevant parameter regime along with a possible superconducting instability of the spin-polarised band resulting in a topological superconductor.