The orbital degrees of freedom refer to different shapes of the wave functions with degenerate energies. In recent years, optical lattices engineered by interfering laser beams offer new means to explore interacting fermions with orbital degrees of freedom the symmetries of which differ from those found in traditional solids. We show that the orbital hopping pattern alone is sufficient for producing topologically non-trivial band structures. We unveil a topological insulator phase of fermions on a two-leg ladder of double-well lattices, similar to those recently realized in experiments.

Topological orbital ladders, Xiaopeng Li, Erhai Zhao, W. Vincent Liu, arXiv:1205.0254