Intense-Laser Nondipole-Induced Symmetry Breaking in Solids

Abstract

High-harmonic spectroscopy in solids gives insight into the inner workings of solids, such as reconstructing band structures or probing the topological phase of materials. High-harmonic generation (HHG) is a highly non-linear phenomena and simulations guide interpretation of experimental results. These simulations often rely on the electric dipole approximation, even though the driving fields enter regimes that challenge its accuracy. Here, we investigate effects of including nondipole terms in the light-matter coupling in simulations of HHG in materials with both topologically trivial and non-trivial phases. We show how the inclusion of nondipole terms breaks dipole selection rules, allowing for new polarizations of the generated light. Specifically we find that helicity, completely absent in the dipole approximation, is induced by the nondipole extension, and that this helicity is dependent on the topological phase of the material.

Figures (4)

• Figure 1: Harmonic spectra of graphene for a driving laser with $\lambda = 3 \ \mu$m, polarized along the $\Gamma-K$ direction. (a) Spectrum polarized along $\Gamma - M$ with overlapping ED and ND contributions. (b) Spectrum along $\Gamma - K$ showing that only ND contributes. The ND driving laser breaks the reflection axis about $\Gamma - M$, and thus allows for polarization along $\Gamma-K$.
• Figure 2: (a) and (b) Ellipticity dependence of the generated light with varying on-site potential, starting from graphene at $\Delta_A = 0$ and ending at hBN at $\Delta_A = 2.81$ eV for ED and ND fields, respectively. (c) ND ellipticity increase with driving field wavelength for $\Delta_A = 0.562$ eV.
• Figure 3: Harmonic spectra of the Kane-Mele model. (a) Spectrum polarized along $\Gamma-M$ with overlapping ED and ND spectra. (b) Spectrum polarized along $\Gamma-K$ with only a ND contribution. Like with graphene, the symmetry-breaking nature of the ND field can be seen by breaking the ED selection rule and allowing for the emitted light to be polarized along $\Gamma-K$.
• Figure 4: Helicity measurements of the Kane-Mele spectra for ED and ND driving lasers. As the Kane-Mele model is TR invariant like graphene, we break this symmetry with the ND driving laser. In the case of the ED driving laser the helicity is always strictly 0, but for the ND driver it is parameter dependent. The dotted line in (b) indicates the point of topological phase transition.