  Based on random phase approximation (RPA), we numerically calculate dynamical
structure factors of a balanced two-dimensional (2D) Fermi superfluid, and
discuss their energy, momentum and interaction strength dependence in the 2D
BEC-BCS crossover. At a small transferred momentum, a stable Higgs mode is
observed in the unitary 2D Fermi superfluid gas where the particle-hole
symmetry is not satisfied. Stronger interaction strength will make the
visibility of the dispersion of Higgs mode harder to be observed. We also
discuss the dimension effect and find that the signal of the Higgs mode in two
dimension is more obvious than that in 3D case. At a large transferred momentum
regime, stronger interaction strength will induce the weight of the molecules
excitation increasing, while in verse the atomic one decreasing, which shows
the pairing information of Fermi superfluid. The theoretical results
qualitatively agree with the corresponding Quantum Monte Carlo data.
