# CAMP: Topological and strong correlation physics in the px/py-orbital bands of the honeycomb lattice – from solid states to optical lattices

## Main Content

Different from graphene which is usually orbitally inactive, the p$_{x,y}$-orbital band in the 2D honeycomb lattice is orbitally active which exhibits a variety of novel topological and strong correlation physics. The interplay between the orbital structure and spin-orbit coupling gives rise to the 2D quantum spin Hall state and quantum anomalous Hall state with large values of topological gaps. The gap values are equal to the atomic level spin-orbit coupling strength, and thus are much larger than those based on the mechanism of the* s-p* band inversion. The energy spectra and eigen-wavefunctions are solved analytically based on Clifford algebra, which greatly facilitates the topological analysis. Flat bands also naturally arise and the consequential non-perturbative physics includes Wigner crystallization and ferromagnetism. In the Mott-insulating state, orbital exchange is highly frustrated described by a quantum 120$^\circ$ model in a similar form to the celebrated Kitaev model. We will show that an f-wave Cooper pairing arises if the band is filled with spinless fermions exhibiting boundary Majorana modes. Although the pairing mechanism is conventional, the unconventional pairing symmetry is driven by the non-trivial band structure. We will also show that the above physics in optical lattices is closely connected to the recent progress in several classes of solid state materials including organic materials, fluoridated tin film, germanene. BiX/SbX(X=H, F, Cl, Br), etc.

Selected References

1. Gu-Feng Zhang, Yi Li, Congjun Wu, ,The honeycomb lattice with multi-orbital structure: topological and quantum anomalous Hall insulators with large gaps ,Phys. Rev. B 90, 075114 (2014) .

2. Wei-cheng Lee, Congjun Wu, and S. Das Sarma, "$F$-wave pairing of cold atoms in optical lattices", Phys. Rev. A 82, 053611 (2010).

3. Congjun Wu, "Orbital analogue of quantum anomalous Hall effect in $p$-band systems", Phys. Rev. Lett. 101, 186807 (2008).

4. Congjun Wu, "Orbital orderings and frustrations of p-band systems in optical lattices", Phys. Rev. Lett. 100, 200406 (2008).

5. Congjun Wu, Doron Bergman, Leon Balents, and S. Das Sarma, "Flat bands and Wigner crystallization in the honeycomb optical lattice", Phys. Rev. Lett. 99, 70401 (2008).