  We investigate the interaction-driven instability of a quadratic band
crossing arising for ultracold bosonic atoms loaded into a two-dimensional
optical lattice. We consider the case when the degenerate point becomes a local
minimum of both crossing energy bands such that it can support a stable
Bose-Einstein condensate. Repulsive contact interaction among the condensed
bosons induces a spontaneously time-reversal symmetry broken superfluid phase
and a topological gap is opened in the excitation spectrum. We propose two
concrete realizations of the desired quadratic band crossing in lattices with
either fourfold or sixfold rotational symmetries via suitable tuning of the
unit cell leading to reduced Brillouin zones and correspondingly folded bands.
In either case, topologically protected edge excitations are found for a finite
system.
