Probing the Electronic Band Gap of Solid Hydrogen by Inelastic X-Ray Scattering up to 90 GPa

Metallization of hydrogen as a key problem in modern physics is the pressure-induced evolution of the hydrogen electronic band from a wide-gap insulator to a closed gap metal. However, due to its remarkably high energy, the electronic band gap of insulating hydrogen has never before been directly observed under pressure. Using high-brilliance, high-energy synchrotron radiation, we developed an inelastic x-ray probe to yield the hydrogen electronic band information in situ under high pressures in a diamond-anvil cell. The dynamic structure factor of hydrogen was measured over a large energy range of 45 eV. The electronic band gap was found to decrease linearly from 10.9 to 6.57 eV, with an 8.6 times densification ($\rho /{\rho }_0\sim 8.6$) from zero pressure up to 90 GPa.

Figure 1

Schematic drawings showing typical (a) optical and (b)–(d) IXS geometries using a DAC; (a)–(c) side view and (d) top view are not drawn to scale. The red lines in (b) and (d) show the narrowly focused incident x-ray beam passing through the blue hydrogen sample while avoiding the diamond anvils on top and bottom (b), and gasket on the side (d). (c) the diamond anvil was moved $100\mu \mathrm{m}$ vertically to collect signal from the diamond background and (d) the dotted line shows the DAC was moved $150\mu \mathrm{m}$ sideways to collect the Be gasket background. An x-ray confocal “polycapillary” device is used to select the signal coming from the rhomboid-shaped (light blue colored) portion of the hydrogen sample.

Figure 2

IXS spectra of (a) solid hydrogen, (b) Be gasket, and (c) diamond anvil at 6.6 GPa. The off-scale peak at zero energy loss is the elastic peak of the incident x ray.

Figure 3

(a) IXS spectra of solid hydrogen at high pressures from 6.6 to 90.2 GPa. The inset photomicrograph shows the $100\mu \mathrm{m}$ hydrogen sample at 90.2 GPa. (b) The band gap of solid hydrogen determined at the breaking points of the slopes of the IXS spectra (illustrated in the insets); blue, experiments at APS; red, experiments at SSRF; seven different solid symbols represent separate DAC IXS experiments; open square, the zero pressure ($<{10}^{-7}\mathrm{torr}$), low temperature (2 K) threshold energy from Ref. [11]; open circles, theoretical calculations; solid line, linear regression of the IXS experimental data.

Figure 4

Threshold energy of solid hydrogen from IXS as a function of density and pressure. The open square corresponds to the zero pressure ($<{10}^{-7}\mathrm{torr}$), low temperature (2 K) threshold energy from Ref. [11]. Open circles represent the data from theoretical calculations in this work. Filled black circles are IXS data from this work compared with experimental data from Van Straaten [12] (upward triangles), Hemley [13] (downward triangles), Garcia [14] (left triangles), Howie [15] (right triangles), Goncharov [16] (hexagons), Loubeyre [17] (diamonds), Zha [18] (stars), and Loubeyre [6] (open diamonds). The shade areas show the scattering of the data set with the same color hues. The dotted line shows the trend of band-gap closure as a guide for the eye.