Unavoidable Gapless Boundary State and Boundary Superfluidity of Trapped Bose Mott States in Two-Dimensional Optical Lattices

We study the boundary nature of trapped bosonic Mott insulators in optical square lattices, by performing quantum Monte Carlo simulation. We show that a finite superfluid density generally emerges in the incommensurate-filling (IC) boundary region around the bulk Mott state, irrespectively of the width of the IC region. Both off-diagonal and density correlation functions in the IC boundary region exhibit a nearly power-law decay. The power-law behavior and superfluidity are well developed below a characteristic temperature. These results indicate that a gapless boundary mode always emerges in any atomic Mott insulators on optical lattices. This further implies that if we consider a topological insulating state in Bose or Fermi atomic systems, its boundary possesses at least two gapless modes (or coupled modes) of an above IC edge state and the intrinsic topologically-protected edge state.