Electronic Structure of Crystalline ${}^4\mathrm{He}$ at High Pressures

Using inelastic x-ray scattering techniques, we have succeeded in probing the high-pressure electronic structure of helium at 300 K. Helium has the widest known valence-conduction band gap of all materials a property whose high-pressure response has been inaccessible to direct measurements. We observed a rich electron excitation spectrum, including a cutoff edge above 23 eV, a sharp exciton peak showing linear volume dependence, and a series of excitations and continuum at 26 to 45 eV. We determined the electronic dispersion along the $\Gamma \mathrm{\text{−}}M$ direction over two Brillouin zones, and provided a quantitative picture of the helium exciton beyond the simplified Wannier-Frenkel description.

Figure 1

${}^4\mathrm{He}$ zone-center IXS spectra and background at 13.4 GPa. The raw spectrum contains a background contribution from Be and diamond. The Be gasket spectrum shows a typical metallic character with the initial slope taking off from zero energy loss. The diamond spectrum shows a gap with initial slope taking off above 10 eV. The backgrounds are subtracted by matching slopes of the raw spectrum at zero and 10 eV with a fraction of the Be and diamond spectra to obtain the net ${}^4\mathrm{He}$ IXS spectrum.

Figure 2

${}^4\mathrm{He}$ zone-center IXS spectra at high pressures. To avoid the intense elastic scattering from the 100 Bragg diffraction, our measurements were taken slightly off the $\Gamma$ point at $2\theta =40°$, corresponding to $q^{*}=0.992$, 0.998, and 0.972 for 11.9, 13.4, and 17 GPa, respectively. Inset: exciton peak position as a function of volume.

Figure 3

Experimental (left) and theoretical (right) IXS spectra of ${}^4\mathrm{He}$ at the volume of $4.170{\mathrm{cm}}^3/\mathrm{mol}$. Dispersion along the $h00$ direction, IXS spectra are shown with scattering angle from 25° to 90° in 5° steps and 90° to 130° in steps of 20°. Dotted gray lines are a guide for the eye.

Figure 4

Dispersion of the ${}^4\mathrm{He}$ exciton along periodic Brillouin zone $\Gamma$ ($q^{*}=1$ and 2) to $M$ ($q^{*}=0.5$ and 1.5) at the volume of $4.170{\mathrm{cm}}^3/\mathrm{mol}$.