Minimum metallic conductivity of fluid hydrogen at 140 GPa (1.4 Mbar)

Abstract

Electrical conductivity measurements indicate that fluid hydrogen achieves the minimum conductivity of a metal at 140 GPa, ninefold initial liquid-${\mathrm{H}}_{2}$ density, and 2600 K. Metallization density is defined to be that at which the electronic mobility gap ${E}_{g}$ is reduced by pressure to ${E}_{g}\ensuremath{\sim}{k}_{B}T,$ at which point ${E}_{g}$ is filled in by fluid disorder to produce a metallic density of states with a Fermi surface and the minimum conductivity of a metal. High pressures and temperatures were obtained with a two-stage gun, which accelerates an impactor up to 7 km/sec. A strong shock wave is generated on impact with a holder containing liquid hydrogen at 20 K. The impact shock is split into a shock wave reverberating in hydrogen between two stiff ${\mathrm{Al}}_{2}{\mathrm{O}}_{3}$ anvils. This compression heats hydrogen quasi-isentropically to about twice its melting temperature and lasts \ensuremath{\sim}100 ns, sufficiently long to achieve equilibrium and sufficiently short to preclude loss of hydrogen by diffusion and chemical reactions. The measured conductivity increases four orders of magnitude in the range 93 to 140 GPa and is constant at 2000 (\ensuremath{\Omega} ${\mathrm{c}\mathrm{m})}^{\mathrm{\ensuremath{-}}1}$ from 140 to 180 GPa. This conductivity is that of fluid Cs and Rb undergoing the same transition at 2000 K. This measured value is within a factor of 5 or less of hydrogen conductivities calculated with (i) minimum conductivity of a metal, (ii) Ziman model of a liquid metal, and (iii) tight-binding molecular dynamics. At metallization this fluid is \ensuremath{\sim}90 at. % ${\mathrm{H}}_{2}$ and 10 at. % H with a Fermi energy of \ensuremath{\sim}12 eV. Fluid hydrogen at finite temperature undergoes a Mott transition at ${D}_{m}^{1/3}{a}^{*}=0.30,$ where ${D}_{m}$ is the metallization density and ${a}^{*}$ is the Bohr radius of the molecule. Metallization occurs at a lower pressure in the fluid than predicted for the solid probably because crystalline and orientational phase transitions in the ordered solid do not occur in the fluid and because of many-body and structural effects. Tight-binding molecular dynamics calculations by Lenosky et al. suggest that fluid metallic hydrogen is a novel state of condensed matter. Protons are paired transiently and exchange on a timescale of a few molecular vibrational periods, $\ensuremath{\sim}{10}^{\ensuremath{-}14}\mathrm{sec}.$ Also, the kinetic, vibrational, and rotational energies of the dynamically paired protons are comparable.