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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We theoretically investigate high-order harmonic generation (HHG) from solids in two-color fields. It is found that under the premise of maintaining the same amplitude, the intensity of the second plateau can be enhanced by two to three orders in a proper two-color field compared with the result in the monochromatic field with the same frequency as the driving pulse of the two-color field. This can be attributed to the fact that most excited electrons can be driven to the top of the first conduction band due to the larger vector potential of the two-color fields, which leads to the higher electron population of upper conduction bands. Moreover, we also find that isolated attosecond pulses can be generated from solids by choosing a proper two-color field that allows the electrons to reach the top of the first conduction band only once. This work provides a promising method for extending the range of solid HHG spectra in experiments.

Quantum Hall (QH) states are arguably the most ubiquitous examples of nontrivial topological order, requiring no special symmetry and elegantly characterized by the first Chern number. Their higher dimension generalizations are particularly interesting from both mathematical and phenomenological perspectives, and have attracted recent attention due to high profile experimental realizations [1, 2]. In this work, we derive from first principles the electromagnetic response of QH systems in arbitrary number of dimensions, and elaborate on the crucial roles played by their modified phase space density of states under the simultaneous presence of magnetic field and Berry curvature. We provide new mathematical results relating this phase space modification to the noncommutativity of phase space, and show how they are manifested as a Hall conductivity quantized by a higher Chern number. When a Fermi surface is present, additional response currents unrelated to these Chern numbers also appear. This unconventional response can be directly investigated through a few minimal models with specially chosen fluxes. These models, together with more generic 6D QH systems, can be realized in realistic 3D experimental setups like cold atom systems through possibly entangled synthetic dimensions.

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