Bogoliubov excitations in a Bose–Hubbard model on a hyperhoneycomb lattice**Project supported by the National Natural Science Foundation of China (Grant Nos. 11474025, 11674026, and 11504285), Specialized Research Fund for the Doctoral Program, China, and Young Talent Fund of University Association for Science and Technology in Shaanxi, China (Grant No. 20160224).

Abstract

We study the topological properties of Bogoliubov excitation modes in a Bose–Hubbard model of three-dimensional (3D) hyperhoneycomb lattices. For the non-interacting case, there exist nodal loop excitations in the Bloch bands. As the on-site repulsive interaction increases, the system is first driven into the superfluid phase and then into the Mott-insulator phase. In both phases, the excitation bands exhibit robust nodal-loop structures and bosonic surface states. From a topology point of view, these nodal-loop excitation modes may be viewed as a permanent fingerprint left in the Bloch bands.