Origin of flat bands in three-dimensional coupled kagome lattices

Two-dimensional kagome lattices are known to host a flat band and Dirac point due to the destructive quantum interference of electronic wavefunctions [1-3]. In this work, we have introduced an exact analytical decimation transformation scheme to explore the coexistence of flat band and Dirac point in three-dimensional coupled kagome systems. Our proposed technique allows coarse-graining of the parameter space, which maps the original system to an analogous low-level lattice [4]. The decimated system facilitates defining a descriptor that controls the appearance of a flat band and provides a definite criterion for absolute flatness. We confirm our predictions on the emergence of the flat band and Dirac points for a class of materials employing material databases in conjunction with density functional theory calculations. The present work explores the intricate electronic properties of coupled kagome lattices and provides an analytical formalism that can efficiently investigate the rich physics of such lattice models.

References:

1. [1] Bergman, D.L. et. al., Physical Review B, 78(12), p.125104 (2008).
   
   [2] Kang, M. et.al., Nature materials, 19(2), pp.163-169 (2020).
   
   [3] Kang, M. et. al., Nature communications, 11(1), p.4004 (2020).
   
   [4] Sil, S. et. al., Physical review letters, 101(7), p.076803 (2008).