  We theoretically study high-harmonic generation (HHG) from solids driven by
intense laser pulses using a one-dimensional model periodic crystal. By
numerically solving the time-dependent Schr\"{o}dinger equation directly on a
real-space grid, we successfully reproduce experimentally observed unique
features of solid-state HHG such as the linear cutoff-energy scaling and the
sudden transition from a single- to multiple-plateau structure. Based on the
simulation results, we propose a simple model that incorporates
vector-potential-induced intraband displacement, interband tunneling, and
recombination with the valence-band hole. One key parameter is the
valley-to-peak amplitude of the pulse vector potential, which determines the
crystal momentum displacement during the half cycle. When the maximum
peak-to-valley amplitude $A_{\rm peak}$ reaches the half width $\frac{\pi}{a}$
of the Brillouin zone with $a$ being the lattice constant, the HHG spectrum
exhibits a transition from a single- to multiple-plateau structure, and even
further plateaus appear at $A_{\rm peak} = \frac{2\pi}{a}, \frac{3\pi}{a},
\cdots$. The multiple cutoff positions are given as functions of $A_{\rm peak}$
and the second maximum $A_{\rm peak}^{\prime}$, in terms of the energy
difference between different bands. Using our recipe, one can draw electron
trajectories in the momentum space, from which one can deduce, for example, the
time-frequency structure of HHG without elaborate quantum-mechanical
calculations. Finally, we reveal that the cutoff positions depend on not only
the intensity and wavelength of the pulse, but also its duration, in marked
contrast to the gas-phase case. Our model can be viewed as a solid-state and
momentum-space counterpart of the familiar three-step model, highly successful
for gas-phase HHG, and provide a unified basis to understand HHG from
solid-state materials and gaseous media.
