XYZ HONEYCOMB

LITOn the honeycomb lattice each site has three bonds. In graphene, electrons hopping along them give Dirac cones where the bands touch at the K points. In Kitaev's exactly solvable model (2006) each bond direction couples a different spin component (x, y or z). The ground state is a quantum spin liquid whose excitations are Majorana fermions and, in a field, non-Abelian anyons, a route to topological qubits. α-RuCl₃ is the leading candidate: Kasahara et al. (Nature 559, 227, 2018) reported a half-quantized thermal Hall effect. Later work (Bruin et al., Nat. Phys. 18, 401, 2022) found a plateau near half-quantization above about 10 T, but whether it is truly quantized is still debated. α-RuCl₃ also orders as a zigzag antiferromagnet below about 7.5 K.

MODEL · COMPUTEDThe bonds glow in their Kitaev colours. A random spin flip creates a pair of flux "vortices" (the plaquettes whose bond-product flips), which wander and annihilate: the emergent particles of the spin liquid, drawn schematically. Right: graphene's |E(k)| on the Brillouin zone, dark at the six Dirac points (computed).

flip a bondanneal

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