Conductivity and dissociation in liquid metallic hydrogen and implications for planetary interiors

Nonmetal-to-metal transition in liquid hydrogen using density functional theory and the Heyd-Scuseria-Ernzerhof exchange-correlation functional

We investigate the first-order liquid-liquid phase transition in fluid hydrogen, which is accompanied by a nonmetal-to-metal transition. We use a combination of density functional theory for the electrons and molecular dynamics simulations for the ions. By employing the nonlocal Heyd-Scuseria-Ernzerhof exchange-correlation functional, we accurately determine the equation of state and the corresponding coexistence line. Additionally, we calculate the electrical conductivity using the Kubo-Greenwood formula and find jumps in the coexisting region, which is characteristic of a first-order transition. Our new predictions are compared with previous theoretical results and available experimental data. Thereby, we find that the strongly constrained and appropriately normed exchange-correlation functional provides an excellent balance between computational cost and accuracy.

Theoretical evidence of H-He demixing under Jupiter and Saturn conditions

The immiscibility of hydrogen-helium mixture under the temperature and pressure conditions of planetary interiors is crucial for understanding the structures of gas giant planets (e.g., Jupiter and Saturn). While the experimental probe at such extreme conditions is challenging, theoretical simulation is heavily relied in an effort to unravel the mixing behavior of hydrogen and helium. Here we develop a method via a machine learning accelerated molecular dynamics simulation to quantify the physical separation of hydrogen and helium under the conditions of planetary interiors. The immiscibility line achieved with the developed method yields substantially higher demixing temperatures at pressure above 1.5 Mbar than earlier theoretical data, but matches better to the experimental estimate. Our results suggest a possibility that H-He demixing takes place in a large fraction of the interior radii of Jupiter and Saturn, i.e., 27.5% in Jupiter and 48.3% in Saturn. This indication of an H-He immiscible layer hints at the formation of helium rain and offers a potential explanation for the decrease of helium in the atmospheres of Jupiter and Saturn.

Exciton Nature of Plasma Phase Transition in Warm Dense Fluid Hydrogen: ROKS Simulation

The transition of warm dense fluid hydrogen from an insulator to a conducting state at pressures of about 20-400 GPa and temperatures of 500-5000 K has been the subject of active scientific research over the past few decades. However, various experimental and theoretical methods do not provide consistent results. In this work, we have applied the restricted open-shell Kohn-Sham (ROKS) method for first principles molecular dynamics of dense hydrogen after thermal excitation to the first singlet excited state. The Wannier localization method has allowed us to analyze the exciton dynamics in this system. The model shows that a key mechanism of the transition is associated with the dissociation of electron-hole pairs, which allows explaining several stages of the transition of fluid H₂ from molecular state to plasma. This mechanism is able to give a quantitative description of several experimental results as well as to resolve the discrepancies between experimental studies.

Thermodynamic modeling of fluid polyamorphism in hydrogen at extreme conditions

Fluid polyamorphism, the existence of multiple amorphous fluid states in a single-component system, has been observed or predicted in a variety of substances. A remarkable example of this phenomenon is the fluid–fluid phase transition (FFPT) in high-pressure hydrogen between insulating and conducting high-density fluids. This transition is induced by the reversible dimerization/dissociation of the molecular and atomistic states of hydrogen. In this work, we present the first attempt to thermodynamically model the FFPT in hydrogen at extreme conditions. Our predictions for the phase coexistence and the reaction equilibrium of the two alternative forms of fluid hydrogen are based on experimental data and supported by the results of simulations. Remarkably, we find that the law of corresponding states can be utilized to construct a unified equation of state combining the available computational results for different models of hydrogen and the experimental data.

Modeling fluid polyamorphism through a maximum-valence approach

We suggest a simple model to describe polyamorphism in single-component fluids using a maximum-valence approach. The model contains three types of interactions: (i) Atoms attract each other by van der Waals forces that generate a liquid-gas transition at low pressures, (ii) atoms may form covalent bonds that induce association, and (iii) atoms with maximal valence attract or repel each other stronger than other atoms, thus generating liquid-liquid separation. As an example, we qualitatively compare this model with the behavior of liquid sulfur and show that condition (iii) generates a liquid-liquid phase transition in addition to the liquid-gas phase transition.

Isotope Quantum Effects in the Metallization Transition in Liquid Hydrogen

Quantum effects in condensed matter normally only occur at low temperatures. Here we show a large quantum effect in high-pressure liquid hydrogen at thousands of Kelvins. We show that the metallization transition in hydrogen is subject to a very large isotope effect, occurring hundreds of degrees lower than the equivalent transition in deuterium. We examined this using path integral molecular dynamics simulations which identify a liquid-liquid transition involving atomization, metallization, and changes in viscosity, specific heat, and compressibility. The difference between H_{2} and D_{2} is a quantum mechanical effect that can be associated with the larger zero-point energy in H_{2} weakening the covalent bond. Our results mean that experimental results on deuterium must be corrected before they are relevant to understanding hydrogen at planetary conditions.

Internal resistive heating of non-metallic samples to 3000 K and >60 GPa in the diamond anvil cell

High pressure-temperature experiments provide information on the phase diagrams and physical characteristics of matter at extreme conditions and offer a synthesis pathway for novel materials with useful properties. Experiments recreating the conditions of planetary interiors provide important constraints on the physical properties of constituent phases and are key to developing models of planetary processes and interpreting geophysical observations. The laser-heated diamond anvil cell (DAC) is currently the only technique capable of routinely accessing the Earth's lower-mantle geotherm for experiments on non-metallic samples, but large temperature uncertainties and poor temperature stability limit the accuracy of measured data and prohibits analyses requiring long acquisition times. We have developed a novel internal resistive heating (IRH) technique for the DAC and demonstrate stable heating of non-metallic samples up to 3000 K and 64 GPa, as confirmed by in situ synchrotron x-ray diffraction and simultaneous spectroradiometric temperature measurement. The temperature generated in our IRH-DAC can be precisely controlled and is extremely stable, with less than 20 K variation over several hours without any user intervention, resulting in temperature uncertainties an order of magnitude smaller than those in typical laser-heating experiments. Our IRH-DAC design, with its simple geometry, provides a new and highly accessible tool for investigating materials at extreme conditions. It is well suited for the rapid collection of high-resolution P-V-T data, precise demarcation of phase boundaries, and experiments requiring long acquisition times at high temperature. Our IRH technique is ideally placed to exploit the move toward coherent nano-focused x-ray beams at next-generation synchrotron sources.

Evidence for supercritical behaviour of high-pressure liquid hydrogen

Hydrogen, the simplest and most abundant element in the Universe, develops a remarkably complex behaviour upon compression¹. Since Wigner predicted the dissociation and metallization of solid hydrogen at megabar pressures almost a century ago², several efforts have been made to explain the many unusual properties of dense hydrogen, including a rich and poorly understood solid polymorphism^1,3-5, an anomalous melting line⁶ and the possible transition to a superconducting state⁷. Experiments at such extreme conditions are challenging and often lead to hard-to-interpret and controversial observations, whereas theoretical investigations are constrained by the huge computational cost of sufficiently accurate quantum mechanical calculations. Here we present a theoretical study of the phase diagram of dense hydrogen that uses machine learning to 'learn' potential-energy surfaces and interatomic forces from reference calculations and then predict them at low computational cost, overcoming length- and timescale limitations. We reproduce both the re-entrant melting behaviour and the polymorphism of the solid phase. Simulations using our machine-learning-based potentials provide evidence for a continuous molecular-to-atomic transition in the liquid, with no first-order transition observed above the melting line. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behaviour.

Molecular Simulation of Covalent Bond Dynamics in Liquid Silicon

Many atomic liquids can form transient covalent bonds reminiscent of those in the corresponding solid states. These directional interactions dictate many important properties of the liquid state, necessitating a quantitative, atomic-scale understanding of bonding in these complex systems. A prototypical example is liquid silicon, wherein transient covalent bonds give rise to local tetrahedral order and consequent nontrivial effects on liquid-state thermodynamics and dynamics. To further understand covalent bonding in liquid silicon, and similar liquids, we present an ab initio-simulation-based approach for quantifying the structure and dynamics of covalent bonds in condensed phases. Through the examination of structural correlations among silicon nuclei and maximally localized Wannier function centers, we develop a geometric criterion for covalent bonds in liquid Si. We use this to monitor the dynamics of transient covalent bonding in the liquid state and estimate a covalent bond lifetime. We compare covalent bond dynamics to other processes in liquid Si and similar liquids and suggest experiments to measure the covalent bond lifetime.

Phase diagram of hydrogen at extreme pressures and temperatures; updated through 2019 (Review article)

Hydrogen is expected to display remarkable properties under extreme pressures and temperatures stemming from its low mass and thus propensity to quantum phenomena. Exploring such phenomena remains very challenging even though there was a tremendous technical progress both in experimental and theoretical techniques since the last comprehensive review (McMahon et al.) was published in 2012. Raman and optical spectroscopy experiments including infrared have been extended to cover a broad range of pressures and temperatures (P—T) probing phase stability and optical properties at these conditions. Novel pulsed laser heating and toroidal diamond anvil techniques together with diamond anvil protecting layers drastically improved the capabilities of static compression methods. The electrical conductivity measurements have been also performed to much higher than previously pressures and extended to low temperatures. The dynamic compression techniques have been dramatically improved recently enabling ramp isentropic compression that allows probing a wide range of P–T thermodynamic pathways. In addition, new theoretical methods have been developed beyond a common DFT theory, which make them predictive and in better agreement with experiments. With the development of new theoretical and experimental tools and sample loading methods, the quest for metallic hydrogen accelerated recently delivering a wealth of new data, which are reviewed here.

A Spectroscopic Study of the Insulator-Metal Transition in Liquid Hydrogen and Deuterium

The insulator-to-metal transition in dense fluid hydrogen is an essential phenomenon in the study of gas giant planetary interiors and the physical and chemical behavior of highly compressed condensed matter. Using direct fast laser spectroscopy techniques to probe hydrogen and deuterium precompressed in a diamond anvil cell and laser heated on microsecond timescales, an onset of metal-like reflectance is observed in the visible spectral range at P >150 GPa and T ≥ 3000 K. The reflectance increases rapidly with decreasing photon energy indicating free-electron metallic behavior with a plasma edge in the visible spectral range at high temperatures. The reflectance spectra also suggest much longer electronic collision time (≥1 fs) than previously inferred, implying that metallic hydrogen at the conditions studied is not in the regime of saturated conductivity (Mott-Ioffe-Regel limit). The results confirm the existence of a semiconducting intermediate fluid hydrogen state en route to metallization.

Optical properties of high-pressure fluid hydrogen across molecular dissociation

Optical properties of compressed fluid hydrogen in the region where dissociation and metallization is observed are computed by ab initio methods and compared with recent experimental results. We confirm that at T > 3,000 K, both processes are continuous, while at T < 1,500 K, the first-order phase transition is accompanied by a discontinuity of the dc conductivity and the thermal conductivity, while both the reflectivity and absorption coefficient vary rapidly but continuously. Our results support the recent analysis of National Ignition Facility (NIF) experiments [Celliers PM, et al. (2018) Science 361:677-682], which assigned the inception of metallization to pressures where the reflectivity is ∼0.3. Our results also support the conclusion that the temperature plateau seen in laser-heated diamond-anvil cell (DAC) experiments at temperatures higher than 1,500 K corresponds to the onset of optical absorption, not to the phase transition.

Breakdown of Fermi Degeneracy in the Simplest Liquid Metal

We are reporting the observation of the breakdown of electrons' degeneracy and emergence of classical statistics in the simplest element: metallic deuterium. We have studied the optical reflectance, shock velocity, and temperature of dynamically compressed liquid deuterium up to its Fermi temperature T_{F}. Above the insulator-metal transition, the optical reflectance shows the distinctive temperature-independent resistivity saturation, which is prescribed by Mott's minimum metallic limit, in agreement with previous experiments. At T>0.4 T_{F}, however, the reflectance of metallic deuterium starts to rise with a temperature-dependent slope, consistent with the breakdown of the Fermi surface. The experimentally inferred electron-ion collisional time in this region exhibits the characteristic temperature dependence expected for a classical Landau-Spitzer plasma. Our observation of electron degeneracy lifting extends studies of degeneracy to new fermionic species-electron Fermi systems-and offers an invaluable benchmark for quantum statistical models of Coulomb systems over a wide range of temperatures relevant to dense astrophysical objects and ignition physics.

Saturn’s magnetic field revealed by the Cassini Grand Finale

During 2017, the Cassini fluxgate magnetometer made in situ measurements of Saturn’s magnetic field at distances ~2550 ± 1290 kilometers above the 1-bar surface during 22 highly inclined Grand Finale orbits. These observations refine the extreme axisymmetry of Saturn’s internal magnetic field and show displacement of the magnetic equator northward from the planet’s physical equator. Persistent small-scale magnetic structures, corresponding to high-degree (>3) axisymmetric magnetic moments, were observed. This suggests secondary shallow dynamo action in the semiconducting region of Saturn’s interior. Some high-degree magnetic moments could arise from strong high-latitude concentrations of magnetic flux within the planet’s deep dynamo. A strong field-aligned current (FAC) system is located between Saturn and the inner edge of its D-ring, with strength comparable to the high-latitude auroral FACs.

Insulator-metal transition in dense fluid deuterium

Dense fluid metallic hydrogen occupies the interiors of Jupiter, Saturn, and many extrasolar planets, where pressures reach millions of atmospheres. Planetary structure models must describe accurately the transition from the outer molecular envelopes to the interior metallic regions. We report optical measurements of dynamically compressed fluid deuterium to 600 gigapascals (GPa) that reveal an increasing refractive index, the onset of absorption of visible light near 150 GPa, and a transition to metal-like reflectivity (exceeding 30%) near 200 GPa, all at temperatures below 2000 kelvin. Our measurements and analysis address existing discrepancies between static and dynamic experiments for the insulator-metal transition in dense fluid hydrogen isotopes. They also provide new benchmarks for the theoretical calculations used to construct planetary models.

Metallic hydrogen

Hydrogen is the simplest and most abundant element in the Universe. There are two pathways for creating metallic hydrogen under high pressures. Over 80 years ago Wigner and Huntington predicted that if solid molecular hydrogen was sufficiently compressed in the T  =  0 K limit, molecules would dissociate to form atomic metallic hydrogen (MH). We have observed this transition at a pressure of 4.95 megabars. MH in this form has probably never existed on Earth or in the Universe; it may be a room temperature superconductor and is predicted to be metastable. If metastable it will have an important technological impact. Liquid metallic hydrogen can also be produced at intermediate pressures and high temperatures and is believed to make up ~90% of the planet Jupiter. We have observed this liquid-liquid transition, also known as the plasma phase transition, at pressures of ~1-2 megabar and temperatures ~1000-2000 K. However, in this paper we shall focus on the Wigner-Huntington transition. We shall discuss the methods used to observe metallic hydrogen at extreme conditions of static pressure in the laboratory, extending our understanding of the phase diagram of the simplest atom in the periodic table.

Dynamic conductivity and partial ionization in dense fluid hydrogen

A theoretical description for optical conduction experiments in dense fluid hydrogen is presented. Different quantum statistical approaches are used to describe the mechanism of electronic transport in hydrogen's high-temperature dense phase. We show that at the onset of the metallic transition, optical conduction could be described by a strong rise in atomic polarizability, due to increased ionization, whereas in the highly degenerate limit, the Ziman weak scattering model better accounts for the observed saturation of reflectance. The inclusion of effects of partial ionization in the highly degenerate region provides great agreement with experimental results. Hydrogen's fluid metallic state is revealed to be a partially ionized free-electron plasma. Our results provide some of the first theoretical transport models that are experimentally benchmarked, as well as an important guide for future studies.