Topological phases and fermionic superfluidity on the Lieb lattice

Abstract

The Lieb lattice is an interesting lattice structure that can host interesting topological phases and novel fermionic superfluids. The fact that this two-dimensional lattice has three sites per unit cell, leads to three bands in the spectrum for tight-binding models. An intrinsic spin-orbit coupling term opens gaps between the three bands, which in addition, host a quantum spin Hall effect. The intricate nature of the multi-gap structure opens up the possibility to realize topological phase transitions driven by the next-nearest neighbour hopping t', which are accompanied by a change of spin Chern numbers of the various bands. We envisage a realization of such phenomena in optical lattices under shaking, where the ratio of t' to the next-nearest hopping t can be tuned to, in principle, any value. Finally, we will consider interaction-driven instabilities towards fermionic superfluidity on the Lieb lattice, with a special emphasis on systems with a point-like Fermi surface. Various types of possible superfluids will then be discussed.