Thermal Hall effect and gauge-field picture of magnons in antiferromagnetic skyrmion crystals

Quasiparticle excitations in material solids often experience a fictitious gauge field, which can be a potential source of intriguing transport phenomena. Here, we show that low-energy excitations in insulating antiferromagnetic skyrmion crystals on the triangular lattice are effectively described by magnons with an SU(3) gauge field. The three-sublattice structure in the antiferromagnetic skyrmion crystals is inherited as three internal degrees of freedom for the magnons, which are coupled to their kinetic motion via the SU(3) gauge field that arises from the topologically nontrivial spin texture in real space. We show that the non-commutativity of the SU(3) gauge field breaks an effective time-reversal symmetry and contributes to a magnon thermal Hall effect. We further demonstrate the emergence of the finite thermal Hall conductivity in the antiferromagnetic skyrmion crystals by the linear spin-wave theory. The possible impact of different gauge structures on a thermal Hall conductivity is also discussed.