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Kagome Geometry

Kagome Geometry

Source It is also known as trihexagonal tiling and consists of equilateral triangles and regular hexagons, arranged so that each hexagon is surrounded by triangles and vice versa. Two hexagons and two triangles alternate around each vertex, and its edges form an infinite arrangement of lines.

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The kagome lattice consists of the vertices and edges of the trihexagonal tiling. Despite the name, these crossing points do not form a mathematical lattice.

Note

  • Corner sharing triangles
  • Three sublattices A, B and C
  • Geometric frustration
  • Same space group as Graphene
  • Dirac cones and Flat bands.

kagome_lattice.png

Properties

  • Kagome geometry of corner-sharing triangles plays a special role in condensed-matter physics. In magnetic insulators, it may cause the highly entangled quantum spin liquid state with exotic fractionalized excitation.
  • Kagome metal (also read AV3Sb5 family)exploit another aspect of this peculiar geometry, the simultaneous presence of linear and flat energy bands. The former cross at the Dirac point that gives rise to Weyl nodes (Weyl fermions)when Time reversal symmetry is broken. These interesting features of the electronic structure were detected in several magnetic kagome metals, where spin texture—the type of magnetic order and its individual spin directions—was shown to have large impact on the energy bands and transport.