On Berezinskii-Kosterlitz-Thouless transition in monoaxial chiral helimagnets

We analyze the possibility of Berezinskii-Kosterlitz-Thouless (BKT) transition in XY-model with in-plane Dzyaloshinskii-Moriya (DM) interaction. It is demonstrated that under standard duality transformation of XY-model into the model of two-dimensional Coulomb gas of magnetic vortices, DM interaction is mapped to the effective electric field perpendicular to the original DM vector. Since the electrostatic energy in the constant electric field becomes dominating over the logarithmic Coulomb attraction at sufficiently large length scales, BKT transition is ruled out by the presence of DM interaction. This behavior is confirmed in the renormalization group analysis, which shows that for finite effective electric field the system always flows towards the high temperature phase.