Measurement of the Berry curvature of the real solids

March 2, 2018

A benchmark for further development of ab-initio calculations

High-order harmonic generation (HHG) in solids is an emerging sub-field of ultrafast spectroscopy and attosecond science. There have been reports of HHG from many different materials, for example: ZnO, GaSe, SiO₂, MgO, solid Ar/Kr, MoS₂, Si, metal-sapphire nanostructures and monolayer and multilayer graphene. The rapid development of this sub-field promises new possibilities in investigating electronic properties of solid systems using novel methodologies.
ETH scientists in the group Ultrafast Spectroscopy and Attosecond Science carried our experimental and theoretical works on HHG from different crystallinities of SiO₂. Furthermore, they have performed polarimetry measurements of the emitted extreme ultraviolet radiation to clarify the contributions of different mechanisms involved. The results they acquired have strong implications: (i) it is possible to generate high-energy photons (extending up to 34 eV – 22^nd harmonic order) from standard Ti:Sapphire amplified 30 fs laser pulses and α-quartz. This demonstration enables a possibly next generation of solid-state-based or fiber-based EUV light sources which would be unprecedented in performance and reliability. (ii) They showed two manifestations of symmetry breaking in solids, corresponding to different physical mechanisms: non-vanishing Berry curvature for Γ-M direction and quantum interference of excitation pathways or asymmetric dipole moment for Γ-K direction. By utilizing the semiclassical transport theory including the anomalous velocity, they demonstrated a direct retrieval of the Berry curvature in solids. First ab--initio calculations of the Berry curvature of α-quartz have been performed and the results show a near-quantitative agreement between the retrieved Berry curvature and the calculated Berry curvature of the first conduction band.
Their work not only demonstrate a methodology for direct measurement of Berry curvature in the real solids, serves as a benchmark for further development of ab--initio calculations, but also stimulates applications of the solid-state coherent extreme ultraviolet source in condensed matter physics, photonics, and biology.


 

Figure 1: Unveiling Berry curvature from even-harmonic generation of α-quartz. a, Experimental apparatus showing the spectral measurement with rotatable target and EUV polarizer. b,  Perspective view of the Brillouin zone of α-quartz showing both the Cartesian coordinates as well as k-vectors. c, Projection of the Brillouin zone for a z-cut α-quartz crystal. d, Recorded spectra intensity (false-color) as a function of the rotation angle of the α-quartz sample. The polarizer is fixed at S polarization. The incident electric field is a linearly polarized 30 fs pulse at the carrier wavelength of 800 nm. e,f, Recorded spectra as a function of the rotation angle of the polarizer, when the α-quartz sample is oriented at the Γ-K and Γ-M directions, respectively. Zero degree corresponds to the polarization direction parallel to the incident linearly polarized electric field. Red crosses denote the second order diffraction.

Highlight reference:  Luu, T. T. and H. J. Wörner (2018). Measurement of the Berry curvature of solids using high-harmonic spectroscopy. Nat. Commun. 9: 916. (10.1038/s41467-018-03397-4) Luu-2018.


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