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The Insulator-Metal Transition in Hydrogen

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The Insulator-Metal Transition in Hydrogen COMMENTARY The insulator-metal transition in hydrogen Isaac Silvera1 Lyman Laboratory of Physics, Harvard University, Cambridge, MA 02138 n their pioneering work over 75 years mechanical handling of the electron-ion ago, Wigner and Huntington (1) interaction, and Morales et al. (2) use I predicted that solid molecular hy- amodification called coupled electron-ion drogen would dissociate and become Monte Carlo (CEIMC), with the motion an atomic metal when pressurized to of the nuclei being treated classically. Fi- 25 GPa (25 GPa = 0.25 megabar) at nally, path-integral Monte Carlo (PIMD) a temperature T = 0 K. Subsequently, treats all particles quantum mechanically one of the great challenges of condensed and is the most demanding for computa- matter physics in the past and present tional resources. century has been to achieve metallization Interest in the high-temperature path to of hydrogen. Theory and experiment have metallic hydrogen has grown in recent worked hand in hand. Hydrogen is con- years. A theoretical analysis by Scandolo ceptually the simplest of all atoms, with (3) and Bonev et al. (4) predicted a peak a single proton and electron, doubled in in the melting line of hydrogen and above the molecule, yet it is extremely challeng- this, a line of dissociation to a non- molecular liquid; the peak in the melting ing to theorists. This is mainly because of Fig. 1. A possible phase diagram for hydrogen, the light mass, resulting in large zero-point showing the theoretical melting line and the plasma- line has been observed in static high- motion (i.e., motion of the nuclei of phase transition line. At lower temperatures in the pressure experiments. With increasing a many-body solid at 0 K). To achieve the solid, three phases are observed: hexagonal close pressure beyond the peak, the melting most accurate theoretical results, a full packed (HCP), the broken symmetry phase (BSP), and temperature decreases. Theory is not yet quantum mechanical analysis is required the hydrgrogen A phase (sometimes called I, II, and able to handle the low-temperature regime at all densities and conditions. III). Hydrogen may be liquid-atomic metallic at very at high pressure, but if extrapolated, the Following Wigner and Huntington (1), high pressure and T = 0 K, shown by the extra- melting line may intersect the pressure axis polations (dotted lines). At even higher pressures, at several megabars (Fig.1, dotted line). predictions of the metallization pressure the atomic liquid would solidify. A single shock wave (P) have ranged as high as 20 megabars generates points on the primary Hugoniot, with very Also, by extrapolation, the line for the and currently, are in the range of 4–6 high temperatures but modest pressures; higher transition from liquid-molecular to liquid- megabars. This has been somewhat guided pressures and lower temperatures are achieved off- atomic phase intersects the melting line so by experiment: the highest static pressures Hugoniot with a reverberating shock wave. The that for higher P, solid molecular hydro- achieved with diamond anvil cells have dash-dot line is an isochore. gen melts to liquid-atomic hydrogen. This been ∼3.5 megabar, with hydrogen re- transition from molecular liquid to atomic maining an insulating molecular solid. liquid is called the PPT (discussed below). Further predictions for metallic hydrogen the so-called plasma-phase transition However, in a more recent theoretical are that it would be metastable (i.e., re- (PPT). A possible phase diagram of hy- paper, Tamblyn and Bonev (5) focused on main in the metallic state when pressure is drogen is shown in Fig. 1. the degree of dissociation and do not ob- released), may be a room temperature Theoretical studies have various degrees serve a first-order phase transition. Earlier superconductor, and may even be a liquid of sophistication, and because predictions studies of hot-dense hydrogen using the at 0 K when compressed to the atomic of properties of hydrogen have had a num- CEIMC approach did not detect a first- fl metallic state. To test these predictions, ber of con icting results, it is useful to order phase transition. In the paper by a statically compressed sample at modest classify these. Most modern studies of hy- Morales et al. (2), a finer P,T and density temperatures will be required. drogen use Monte Carlo or molecular- grid are used, and the PPT is observed in A second path to metallization of hy- dynamics simulations requiring substantial three approximations: BOMD, CEIMC, drogen is at high temperature and pres- computing resources. Here, a large number and PIMC. PIMC was only used in a lim- sure in the liquid phase. This region is of particles are allowed to collide or in- ited P-T range. They also calculate the called hot-dense matter and is of particu- teract with each other until they achieve an electrical conductivity, which has the ap- lar interest to planetary scientists; these equilibrium phase. The least demanding pearance of an order parameter for the are the conditions found in the giant outer approach is to use effective pair potentials insulator-metal transition, although it is planets and exoplanets where the dense for each density, but these do not accu- a transport property (2). matter can exist as a plasma. A plasma is rately handle the many-body problem. Next What is a metal, and what is the PPT? a fluid with ionized atoms or molecules. In is Born-Oppenheimer molecular dynamics At low density, atoms or molecules are far a fluorescent lamp, a low-density, low- (BOMD), in which, at each density, the apart with little overlap, and electrons temperature gas of atoms is ionized by an energetics are calculated using density are localized on the atoms so that the applied electric field. At high enough functional theory (DFT). DFT has re- system is insulating. As the density temperatures and pressures in a gas or asonable accuracy and puts increased de- increases, an insulating crystalline solid liquid, a plasma can be formed because mand on computational requirements. A becomes semiconducting with an energy a certain portion of the particles are weakness for hydrogen is that DFT does gap between the valence and conduction thermally ionized and the condensed not handle zero-point motion and under- matter system can electrically conduct. estimates energy bandgaps, important for The article by Morales et al. (2) in PNAS insulator-metal transitions. Quantum Author contributions: I.S. wrote the paper. predicts a first-order phase transition to Monte Carlo (QMC) is more accurate but The author declares no conflict of interest. a metallic phase of liquid atomic hydrogen more demanding on computational re- See companion article on page 12799. at high pressure and temperature. This is quirements; it provides a complete quantum 1E-mail: [email protected]. www.pnas.org/cgi/doi/10.1073/pnas.1007947107 PNAS | July 20, 2010 | vol. 107 | no. 29 | 12743–12744 Downloaded by guest on September 26, 2021 bands; the gap energy is required to excite Hydrogen has an added consideration: deuterium and report a large-density step an electron into the conduction band, thus it is molecular. Although not the first pa- at P ∼ 150 GPa and T ∼ 4,000 K. However, conductivity is 0 at T = 0 K. At sufficiently per, a detailed discussion of the PPT was in this challenging experiment, their data high density and overlap of atoms, the gap presented by Saumon and Chabrier in are sparse, conductivity seems to be mea- closes, and the electrons become delo- 1992 (9). The PPT was predicted to occur sured on another sample, and temperature T calized in the conduction band. At =0K, along with a dissociation transition from and pressure are calculated, and therefore, the electrons can conduct, and the system the molecular to the atomic metallic this does not provide strong evidence of of atoms is a metal. A rigorous experi- phase, first occurring at a temperature ∼ the PPT. mental test for a metal is to show that 15,000 K at the critical point. However, It is interesting to consider an isochore, the electrical conductivity is finite in the shown in Fig. 1. The ionization or metal- T = 0 K limit. This test cannot be carried lization and the dissociation seem to be out for a liquid, because there is no known Morales et al. predict the liquid metal at T = 0 K. Now consider PPT on three different intimately connected. Because the phase hot-dense matter of an atomic system such lines have a negative slope, the density as xenon or helium in the fluid phase. As quantum models. increases as the lines are crossed with in- temperature and density increase, the creasing temperature; within a phase, the fluid goes from insulating state to semi- pressure increases because of increased conducting state to ionized plasma, and more recently, they did not find support thermal pressure. Although the atomic conducting state. With further increase, for the PPT in their effective field model density is constant, in transcending from fi rather than a continuous change, a rst- (10). The PPT is now again predicted, in liquid H2 to atomic H, there are two times order phase transition is predicted to take the work of Morales et al. (2), at much as many particles when molecules dissoci- place, with an abrupt change in density lower temperatures. ate, which results in increased overlap of and degree of ionization. If the atomic Until now, experimental attempts to the particle wave functions, a condition fi overlap is suf cient, the highly ionized observe the PPT have been with shock needed for metallization. state may also be a metal; the term PPT waves.
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