Majorana fermions in Kitaev spin liquids

This chapter reviews Majorana fermions emergent in insulating magnets, particularly the Kitaev quantum spin liquid. The Kitaev model, an S = 1/2 quantum spin model on a honeycomb lattice, can be solved by introducing four Majorana fermions. Three of them consist of local gage fields defined on the bonds of the honeycomb lattice, and they are local conserved quantities. One of the four Majorana fermions moves freely on the lattice under fixed gage fields. Thus, the elementary excitations are governed by the two quasiparticles, itinerant Majorana fermions and local gage fields, which are interpreted as fractionalization of quantum spin. The signatures of the Majorana fermions can be observed in thermodynamic and dynamical properties, such as the specific heat, dynamical spin structure factor, and Raman spectrum. Moreover, the Majorana fermion system becomes topologically nontrivial by applying magnetic fields, and an excited gage field traps an isolated Majorana fermion (Majorana zero mode). This causes a half quantization of thermal Hall coefficient, which should be one of the most demonstrable signatures of the existence of Majorana fermions. Transition metal compounds with strong spin–orbit coupling are proposed as candidate materials whose magnetic properties are dominantly governed by the Kitaev model. Different experimental probes have observed manifestations of Majorana fermions in these materials. However, further investigations are needed in the candidate materials to establish the presence of the Majorana fermions, particularly Majorana zero modes, which can be applied to topological quantum computing.