Origin of flat bands and non-trivial topology in coupled kagome lattices

Abstract The geometric frustration inherent in the kagome lattice gives rise to exotic electronic structures—combining Dirac dispersions, van Hove singularities, and flat bands. Recent discoveries in stacked kagome materials with strong interlayer coupling have reignited questions about the origin and tunability of these distinctive flat bands. In this work, we propose an exact analytical decimation transformation scheme to explore the coexistence of flat bands and Dirac fermions in three-dimensional coupled kagome systems. This method coarse-grains the parameter space, mapping the original system onto an equivalent reduced lattice. The decimated model identifies a key parameter governing flat-band formation and provides a criterion for absolute flatness. In terms of atomic separations, we define a quantity that primarily controls the flat-band width, enabling prediction and tunability in real materials. We validate our framework for the M 3 X (M = Ni, Mn, Co, Fe; X = Al, Ga, In, Sn, Cr, …) family using materials databases and first-principles calculations. This analytical formalism offers a practical route for accurate prediction and design of flat bands in realistic kagome systems.