Intertwined superfluidity and density wave order in a p-orbital Bose condensate

Abstract

We study a continuum model of the weakly interacting Bose gas in the presence of an external field with minima forming a triangular lattice. The second lowest band of the single-particle spectrum (p band) has three minima at nonzero momenta. We consider a metastable Bose condensate at these momenta and find that, in the presence of interactions that vary slowly over the lattice spacing, the order parameter space is isomorphic to S5. We show that the enlarged symmetry leads to the loss of topologically stable vortices, as well as two extra gapless modes with quadratic dispersion. The former feature implies that this non-Abelian condensate is a “failed superfluid” that does not undergo a Berezinskii-Kosterlitz-Thouless (BKT) transition. Order-by-disorder splitting appears suppressed, implying that signatures of the S5 manifold ought to be observable at low temperatures.