Bound states of three fermions forming symmetry-protected topological phases

We propose a simple theoretical construction of certain short-range entangled phases of interacting fermions, by putting the bound states of three fermions (which we refer to as clustons) into topological bands. We give examples in two and three dimensions, and show that they are distinct from any free fermion state. We further argue that these states can be viewed as combinations of certain free fermion topological states and bosonic symmetry-protected topological (SPT) states. This provides a conceptually simple understanding of various SPT phases, and the possibility of realizing them in cold atom systems. New parton constructions of these SPT phases in purely bosonic systems are proposed. We also discuss a related anomaly in two dimensional Dirac theories, which is the gravitational analog of the parity anomaly.

Figure 1

Construction of the cluston Chern insulator: putting the three-fermion clustons into a Chern band.

Figure 2

(a) Construction of the cluston TI: putting the three-fermion clustons into a topological band. (b) Transport signature on a $\mathcal{T}$-breaking surface. ${\sigma }_{xy}-{\kappa }_{xy}=4\left(\mathrm{mod}8\right)$ signifies a nontrivial SPT.