  By studying the 2-dimensional Su-Schrieffer-Heeger-Bose-Hubbard model, we
show the existence of topological Higgs amplitude modes in the strongly
interacting superfluid phase. Using the slave boson approach, we find that, in
the large filling limit, the Higgs excitations and the Goldstone excitations
above the ground state are well decoupled, and both of them exhibit nontrivial
topology inherited from the underlying noninteracting bands. At finite
fillings, they become coupled at high energies; nevertheless, the topology of
these modes are unchanged. Moreover, based on an effective action analysis, we
further provide a universal physical picture for the topological character of
Higgs and Goldstone modes. Our discovery of the first realization of the
topological Higgs mode opens the path to novel investigations in various
systems such as superconductors and quantum magnetism.
