The solid-state harmonic generation (SSHG) derives from photocurrent
coherence. The crystal symmetry, including point-group symmetry and
time-reversal symmetry, constrains the amplitude and phase of the photocurrent,
thus manipulates the coherent processes in SSHG. We revisit the expression of
photocurrent under the electric dipole approximation and give an unambiguous
picture of non-equilibrium dynamics of photocarriers on laser-dressed effective
bands. In addition to the dynamical phase, we reveal the indispensable roles of
the phase difference of transition dipole moments and the phase induced by
shift vector in the photocurrent coherence. Microscopic mechanism of the
selection rule, orientation dependence, polarization characteristics,
time-frequency analysis and ellipticity dependence of harmonics governed by
symmetries is uniformly clarified in our theoretical framework. This work
integrates non-equilibrium electronic dynamics of condensed matter in strong
laser fields, and paves a way to explore more nonlinear optical phenomena
governed by crystal symmetry.Comment: 13 pages,5 figure