Mott insulator–superfluid phase transition in two-band Bose–Hubbard models with gapless nodal lines

Abstract

Recent studies on ultracold atoms have reported the implementation of laser-assisted tunneling in lattice systems, facilitating the realization of topological phases. Motivated by such advances, we investigate a two-band Bose–Hubbard model with its single-particle energy bands showing gapless nodal lines, which can be realized for ultracold atoms in the cubic optical lattices using laser-assisted tunneling. We analyze the superfluid–Mott insulator (MI) phase transition in this model and obtain a global phase diagram by using the strong-coupling expansion method. The excitation spectra in strong and weak coupling limits inherit the topological properties of single-particle energy bands to show the structures of nodal lines. The topological invariants, the flat surface states and the critical properties are analyzed theoretically in detail. The excitation spectra in the MI and superfluid phases are measurable in ultracold atom experiments to prove our results.