Surface chiral Abelian topological order on multilayer cluster Mott insulators

The surface states of a symmetry protected topological state can have many possibilities. Here, we propose a chiral Abelian topological order on a distinct surface of a multilayer-stacked cluster Mott insulating system. The first-principle calculation and the slave-rotor mean-field theory are applied to study the surface states of the relevant material system. The angle-resolved photoemission spectroscopic measurement is further suggested to detect the anomalous surface fractionalization of the chiral Abelian topological order on the surface. The connection with real materials is further discussed. We expect our results to inspire the interest in the emergent exotic and correlation physics among the cluster Mott insulating systems and in the interplay between the two different branches of topological phases.