Intertwined Superfluid and Density Wave Order in a $p$-Orbital Bose Condensate

TL;DR

This paper investigates a weakly interacting Bose gas in a triangular lattice with a focus on a $p$-band condensate, revealing an enlarged symmetry that affects topological stability and superfluid properties.

Contribution

It introduces a continuum model showing an $S^5$ order parameter space in a $p$-orbital Bose condensate, highlighting novel symmetry and topological features.

Findings

Loss of topologically stable vortices

Presence of two extra gapless modes with quadratic dispersion

The condensate acts as a 'failed superfluid' without a BKT transition

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 non-zero 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 $S^{5}$. 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 $S^5$ manifold ought to be observable at low temperatures.