On Thermal Hall Effect in Boson Systems

We theoretically discuss the thermal Hall effect in boson systems keeping in mind possible applications to magnetically ordered insulators with skyrmion lattice ground state. The magnon spectrum of such systems may undergo a topological transition upon the variation of magnetic field, and thermal Hall effect could be a tool to confirm this phenomenon. We rederive formulas, suitable for our purposes, and find expressions which have a different temperature dependence of thermal Hall effect as compared to previously reported results. Particularly, in presence of anomalous terms in magnon Hamiltonian the thermal Hall conductivity has a small but finite residual 1/ T contribution. Such contribution may become sizable at very low temperatures and resembles Meissner effect in superconducting metals.