Bose-Einstein-condensed Cold Atoms in a Lattice System with K-space Berry Curvature

In this paper we study the properties of cold bosons in two-dimensional optical lattices where Bose condensation occurs at a momentum point $\\mathbf{k}$ with nonzero $k$-space Berry curvature. By combining results from both analytic and numerical approaches, the bulk and edge excitation spectra of the system are derived. We show that the boson system carries nonuniversal, nontopological temperature-dependent equilibrium angular momentum and edge current at low temperatures. The differences between boson systems with real- and $k$-space Berry curvature are pointed out. In particular, using a simple variational wave-function approach, we show that for bosons in a harmonic trap, the stability of the Bose-condensed state towards vortex formation is rather different in the two cases because of the different angular momentum scalings in the ground states.