Kagome

LITThe kagome lattice, corner-sharing triangles named after a Japanese basket weave, is geometrically frustrated. Its nearest-neighbour tight-binding model has one perfectly flat band: electrons trapped on hexagonal rings by destructive interference. Kang et al. (Nat. Commun. 11, 4004, 2020) saw a topological flat band in the kagome metal CoSn by ARPES; spin–orbit coupling opens an 80 meV gap at its touching point. Flat bands are a stage for strong correlation.

MODEL · COMPUTEDLeft: the lattice, with a compact localized state that lights up around a chosen hexagon (alternating ± amplitudes). Right: the band structure E(k) diagonalised live along Γ–K–M–Γ. The top band (sign convention here: E = −2t·eigenvalue) sits exactly flat. Add a second-neighbour hopping t′ and watch it bend.

t′/t trap an electron

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