We studied the multi-plateau high-order harmonic generation (HHG) from solids numerically. It is found that the HHG spectrum in the second or higher plateau is redshifted in short laser pulses due to the nonadiabatic effect. The corresponding FWHMs also increase, suggesting the step-by-step excitation process of higher conduction bands in the HHG process. Even order harmonics in the higher plateaus of HHG are present due to the break of symmetry in the k space. It may stimulate related experimental work. High-order harmonic generation (HHG) from gases has been well studied. It has been used to generate attosecond laser pulses [1,2]. It is described by the three-step model [3]. The cutoff energy of HHG is around Ip+3.17Up (Ip is the ionization potential, and Up=A0 2 /4 is the ponderomotive energy). The HHG from bulk crystals has been reported recently [4,5] as the development of long-wavelength lasers. It is quite different from the HHG from gases. The cutoff energy of solid HHG depends on the amplitude of the laser field linearly [4]. It also exhibits multi-plateau structure [6]. However, the mechanisms of HHG from solids are much debated. Inter-and intra-band transitions [4,7,8] are proposed. Three-step model in the coordinate space [9] and vector k space [10] are investigated. Recently, multi-plateau HHG from solids are studied theoretically [7,8,11] and experimentally. Our theoretical model [10] propose that the multi-plateau structure reflects the population of higher conduction bands which are pumped step by step.In the solid systems, even-order harmonics are measured experimentally. They may come from the interference of HHG trajectories in the different valence bands [12]. It may also come from the Berry phase [13]. In this work, we will present a new mechanism for even-order harmonic generation in symmetric periodic potentials.Redshifts of HHG spectra were predicted in the HHG from gases and plasmas [14][15][16][17][18][19][20]. They originate from delayed emission times of HHG from the excited state, resonate state, or dissociation of molecules. It is a nonadiabatic effect. The feature is that most of the HHG signals are generated from the trailing edge of the laser pulse, where dI/dt<0. The driving force from the laser fields is weaker than the previous cycle. The electrons obtain less energy compared to the previous cycle and redshifts of HHG occur. They have been experimentally confirmed [18,[21][22][23]. It was reported that redshift was observed in the optical absorption of crystals in the presence of an intense mid-infrared laser field [24]. In this letter, we find that redshift also exists in emission of HHG from solids. It is universal. The higher conduction bands are excited step by step. As a result, the HHG process in the higher plateau is delayed compared to ultrafast process in the lower conduction bands. As will be shown next, even the system is symmetric in the coordinate space, the electron motion is not symmetric in the k space. Consequently, redshifts of HHG and even-order harmonics ar...