The dependence of high-harmonic generation (HHG) on laser ellipticity is investigated using a modified ZnO model. In the driving of relatively weak field, we reproduce qualitatively the ellipticity dependence as observed in the HHG experiment of wurtzite ZnO. When increasing the field strength, the HHG shows an anomalous ellipticity dependence, similar to that observed experimentally in the single-crystal MgO. With the help of a semiclassical analysis, it is found that the key mechanism inducing the change of ellipticity dependence is the interplay between the dynamical Bloch oscillation and the anisotropic band structure. The dynamical Bloch oscillation contributes additional quantum paths, which are less sensitive to ellipticity. The anisotropic band-structure make the driving pulse with finite ellipticity be able to drive the pairs to the band positions with larger gap, which extends the harmonic cutoff. The combination of these two effects leads to the anomalous ellipticity dependence. The result reveals the importance of dynamical Bloch oscillations for the ellipticity dependence of HHG from bulk ZnO.
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