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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.
We study the topological properties of elementary excitations in a staggered $p_x pm i p_y$ Bose-Einstein condensate realized in recent orbital optical lattice experiments. The condensate wave function may be viewed as a configuration space variant o
We carefully study how the fermion-fermion interactions affect the low-energy states of a two-dimensional spin-$1/2$ fermionic system on the kagom{e} lattice with a quadratic band crossing point. With the help of the renormalization group approach, w
We investigate topological charge pumping in a system of interacting bosons in the tight-binding limit, described by the Rice-Mele model. An appropriate topological invariant for the many-body case is the change of polarization per pump cycle, which
Realizing and characterizing interacting topological phases in synthetic quantum systems is a formidable challenge. Here, we propose a Floquet protocol to realize the antiferromagnetic Heisenberg model with power-law decaying interactions. Based on a
The Leggett collective excitations for a two-band Fermi gas with s-wave pairing and Josephson interband coupling in the BCS-BEC crossover at finite temperatures are investigated within the Gaussian pair fluctuation approach. Eigenfrequencies and damp