Flat bands · macroscopic degeneracy · frustrated geometry
The kagome lattice (named after a Japanese basket weave pattern) consists of corner-sharing triangles — each vertex is shared between two triangles, giving coordination number z=4. Its tight-binding band structure contains a perfectly flat band at E=+2t (one-third of all states), arising from localized eigenstates that can be constructed by destructive interference around the hexagonal loops. This macroscopic degeneracy is exponential in system size and leads to extreme sensitivity to perturbations. The kagome lattice is a playground for flat-band physics, strongly correlated electrons, fractional quantum Hall analogs, and spin liquid ground states (e.g., Herbertsmithite ZnCu₃(OH)₆Cl₂).