Proton tunneling in phase IV of hydrogen and deuterium

Using in situ optical spectroscopy we have investigated the temperature stability of the mixed atomic and molecular phases IV of dense deuterium and hydrogen. Through a series of low-temperature experiments at high pressures, we observe phase III-to-IV transformation, imposing constraints on the P-T phase diagrams. The spectral features of the phase IV-III transition and differences in appearances of the isotopes Raman spectra strongly indicate the presence of proton tunneling in phase IV. No differences between isotopes were observed in absorption spectroscopic studies, resulting in identical values for the band gap. The extrapolation of the combined band gap yields 375 GPa as the minimum transition pressure to the metallic state of hydrogen (deuterium). The minute changes in optical spectra above 275 GPa might suggest the presence of a new solid modification of hydrogen (deuterium), closely related structurally to phase IV.

Figure 1

Representative Raman spectra of deuterium upon cooling (left) and warming (right) showing phase IV-III transformations at 247 and 256 GPa. Inset: Coexistence of the ${\nu }_1$ modes at 300 K and 230 GPa in phases III (higher frequency mode) and IV (lower frequency mode)

Figure 2

(a) Frequency discontinuities of the ${\nu }_1$ modes of H${}_2$ (filled triangles, 262 GPa; filled circles, 242 GPa) and D${}_2$ (open squares, 256 GPa; open diamonds, 247 GPa) across the III-to-IV transformations. (b) FWHM of the ${\nu }_1$ vibrons of H${}_2$ (filled triangles, 262 GPa; filled circles, 242 GPa) and D${}_2$ (open squares, 256 GPa; open diamonds, 247 GPa) plotted versus temperature. Note the quite similar values of FWHM for both isotopes in phase III. Lines in (a) and (b) are guides for the eye only. Inset: FWHM of the H${}_2$ (filled circles) and D${}_2$ (open circles) ${\nu }_1$ vibron versus pressure at 300 K.

Figure 3

Generalized P-T- ${\nu }_1$ diagrams for (a) D${}_2$ and (b) H${}_2$ showing the difference in the vibron frequency landscapes. P-T phase diagrams for (c) D${}_2$ and (d) H${}_2$. The lines separating the phases I, II and III at temperatures below 200 K are from Ref. 9.

Figure 4

Comparison of experimentally observed and theoretically calculated[2] Raman intensities and spectral positions of the hydrogen bands at 250 GPa. (a, b) Experimental raw spectra observed in phases III (a) and IV (b) are shown below (in black); spectra corrected for decreasing sensitivity of the detector are shown above (in red). The broad peaks between 1333 and $\sim$1800 cm${}^{-1}$ are due to the first-order Raman from diamond. (c, d) Experimental renormalized spectra plotted as Gaussian distributions for phases III (c) and IV (d) [vertical (black) lines]; theoretically calculated spectra for (c) $C2/c$ (red) and $Cmca$-12 (blue) and (d) $P_c$ (red). Note that the intensities for renormalized and theoretically calculated spectra are given on a logarithmic scale to show much weaker low-frequency modes and additional vibrational bands besides ${\nu }_1$ and ${\nu }_2$.

Figure 5

Hydrogen and deuterium combined band-gap points (filled squares) as a function of the pressure at 300 K. Dotted (black) straight lines are linear fits to the measured data points in phases IV and IV${}^{\prime }$. Quadratic [upper (red) curve] and cubic [lower (blue) curve] polynomial fits extrapolated to higher pressures are shown as solid lines. Inset: Frequency of the ${\nu }_1$ mode of hydrogen as a function of pressure. Open circles are measured ${\nu }_1$ vibron frequencies versus pressure. The solid (red) line shows the nearly linear (from 275 to 400 GPa) extrapolation of the ${\nu }_1$ frequency up to above 375 GPa—the minimal pressure needed to close the optical band gap. Dashed vertical lines indicate the proposed phase transition between phase IV and phase IV${}^{\prime }$.