Bose-Einstein condensation of Dirac magnons

The discovery of graphene, a two dimensional material which hosts massless linearly dispersive quasiparticles, has led to an extensive research in Dirac fermions in the last decade. The effect of interaction in the stability and renormalization of Dirac cone attracted considerable attention. With the expanding list of fermionic Dirac materials, the idea of bosonic Dirac materials has emerged. In our previous works, we have established the notion of Dirac bosons. In this paper, we analyze and predict the condition for the formation of Bose-Einstein condensation (BEC) by Dirac magnons in Chromium tri-halides CrX₃ (X= Fl, Br and I). The BEC order parameter has a spinor structure and modulates with finite momentum at the Dirac point. We also discuss the dynamics of the two component/spinorial BEC order parameter by a Dirac Gross-Pitaevskii equation. Our work is motivated by a recent experimental observation (PRL 112, 116402 (2014)) of polaritonic Bose-Einstein condensation in honeycomb lattice.