Chiral and helical superfluid in cold atom system

Recently, a chiral spin superfluid has been proposed in weakly interacting boson systems [1]. In this work, we study the properties of bosonic superfluids in a cold atom system with two inequivalent band minima in momentum space related by time reversal symmetry. The system is mapped into an effective spinor-boson model. Without additional symmetries we show that in general there are two possible phases in this model, a ferromagnetic (easy axis) phase and a ``x-y'' (easy plane) phase. In the presence of nonzero k-space Berry curvature at the two band minima points, we show that the ferromagnetic state is ``chiral'' and the x-y state is ``helical.'' The bulk and edge properties of these states are studied where the similarities and differences between the present bosonic superfluids and the corresponding fermionic superconductors are pointed out.\\[4pt] [1] Li, Xiaopeng and Natu, Stefan S and Paramekanti, Arun and Sarma, S Das. ``Chiral spin superfluidity and spontaneous spin Hall effect of interacting bosons.'' \textit{arXiv preprint arXiv:1405.6715}, 2014.