Optical Properties of Fluid Hydrogen at the Transition to a Conducting State

We use fast transient transmission and emission spectroscopies in the pulse laser heated diamond anvil cell to probe the energy-dependent optical properties of hydrogen at pressures of 10–150 GPa and temperatures up to 6000 K. Hydrogen is absorptive at visible to near-infrared wavelengths above a threshold temperature that decreases from 3000 K at 18 GPa to 1700 K at 110 GPa. Transmission spectra at 2400 K and 141 GPa indicate that the absorptive hydrogen is semiconducting or semimetallic in character, definitively ruling out a first-order insulator-metal transition in the studied pressure range.

Figure 1

Phase diagram of hydrogen. Black lines are phase boundaries. Present measurements are filled circles for transparent (white) and absorbing (gray, black) hydrogen; black points are characterized via direct transient absorption measurement (Fig. 2), whereas gray points correspond to anomalous temperature responses observed upon increasing heating laser power (Fig. 3). A thermal pressure of $2.5\mathrm{GPa}/1000\mathrm{K}$ [33] is included. The heavy black line is the onset of absorbing hydrogen in the present data. Prior measurements are the onset of reflectivity in shock compression [14] (crosses and dotted line), the onset of visible absorption in isentropic compression [16] (squares and dashed line), the location of anomalies in temperature with increasing heating laser power in the diamond cell [15] (stars), and the dc conductivity (color map) based on interpolated data [3, 11, 12, 29, 34, 35]. The melting curve is taken from Ref. [28], and the metallization line is the saturation of dc conductivity. White lines are interior conditions of Jupiter [36] and Saturn [37].

Figure 2

Transient absorption and emission measurements in hydrogen at 141 GPa. (a) Laser power (upper panel) and spectrogram showing transient absorption (lower panel). (b) Time histories of absorption at different wavelengths using pulse referencing [34, 38]. (c) Transmission spectrum averaged over $2–5\mu \mathrm{s}$ where absorption (and temperature) is roughly constant. (d) Emission spectrogram (20 spectrograms stacked), with inset showing graybody Planck fit to data at $2–5\mu \mathrm{s}$. Temperature in this time interval was 2400(300) in a series of heat cycles at this laser power. Arbitrary units are a.u.

Figure 3

Temperature histories at 30 GPa with finite element model predictions. Two measurements (open symbols: vertical bars are temperature uncertainty, horizontal bars are time resolution) are presented with finite element models [34, 38, 43] with and without an onset of infrared absorption in hydrogen at a critical temperature of $\sim 3300\mathrm{K}$ (solid and dashed lines, respectively). Below the critical temperature (blue points), models (gray) are indistinguishable and follow behavior typical for a transparent sample with laser energy absorption on the foil surface [43]. For experiments achieving the critical temperature (red points), models (black) show the result of sample absorption: rather than an initial peak and decay that scaled with laser power, temperature is limited to values near the critical temperature [38]. Peak laser power increased from 65 to 155 W between the models. Above 100 GPa transient absorption occurred without this effect, since thinner samples at high pressure did not become infrared-optically thick when heated.

Figure 4

Optical properties of hydrogen. Data at 141 GPa and 2400(300) K are open circles (error bars are systematic), theoretical predictions are crosses, and fits are lines. (a) Absorption spectra with Tauc fits, with theory for semiconducting states at 1600–1700 K, 101–159 GPa [16]. (b) Conductivity spectra with Smith-Drude fits. The dc conductivity corresponding to the present data and used in the fitting is ${\sigma }_0=15\mathrm{S}/\mathrm{cm}$ (triangle). Theory for metal and nonmetal states are for 1000 K, 170 GPa [21]. (c) Smith-Drude backscattering parameter $C$ and (d) scattering time $\tau$ are from theory [17, 21, 23, 24, 34] and this experiment; shaded region in (c) is the conditions for metallization [12, 21, 29] and in (d) the calculated minimum scattering time (Ioffe-Regel limit) [12, 13] for relevant conditions.