  We employ the two-band density-matrix equations and time-dependent density
functional theory to calculate high-order harmonic generation (HOHG) in
graphene under a femtosecond laser irradiation. Our investigation uncovers a
striking harmonic enhancement structure (HES) within a specific energy range of
the HOHG spectrum. In this regime, we find the convergence of multiple
interband electron-hole recombination trajectories, leading to the zero
determinant of the Hessian matrix of the semiclassical action. This trajectory
convergence exhibits the characteristics akin to the focusing behavior of light
rays, commonly known as caustic effects. In contrast to atom situation, where
caustic effects are confined to a narrow energy regime around the HOHG cut-off
energy and the enhancement due to caustic trajectory convergence is less
apparent, the two-dimensional nature of graphene results in a broad energy
region for HOHG enhancement that the caustic trajectories can even dominate the
entire interband harmonic generation regime. The magnitude of enhancement is
significant and can be estimated to be on the order of $\sim N^{2/3}$, with $N$
representing the harmonic order, according to the catastrophe theory. These
mechanisms have broad applicability and hold significant implications for other
two-dimensional materials, as well as bulk materials, providing crucial
insights into the understanding of HOHG phenomena in diverse material systems.
