Metallic Phase Of Hydrogen Research Articles

Superconducting and normal properties of the low-dimensional phases of the metallic hydrogen

In the first part of the paper we consider properties of a two-dimensional low density (n = 1) electron system with strong onsite Hubbard attraction U >W (W is the bandwidth) in the presence of a strong random potential V uniformly distributed in the range from -V to +V. In the framework of the Bogoliubov-de Gennes approach we observed an appearance of inhomogeneous state of spatially separated Fermi-Bose mixture of Cooper pairs and unpaired electrons with the formation of bosonic droplets of different size in the unpaired fermionic matrix. Software package to solve the system of Eliashberg equations that describes the transition of a metal to a superconducting state is presented. We use a version of the Eliashberg system of equations written on the imaginary axis. The system is presented in two versions: without taking into account the corrections for the chemical potential of electrons and with taking them into account. The calculations were performed for the I41/amd phase of metallic hydrogen at a pressure of 500 GPa.

Quantum phase transition in solid hydrogen at high pressure

Extensive experimental and theoretical studies have been devoted to determining the high-pressure phase diagram of hydrogen. We present evidence of a phase at a higher pressure than phase III and below the pressure of the recently observed phase of metallic hydrogen (495 GPa). This phase was determined from infrared (IR) spectroscopy of hydrogen samples at static pressures above 360 \ifmmode\pm\else\textpm\fi{} 15 GPa in a diamond anvil cell, and has been observed in three separate experiments. Whereas earlier studies found new high-pressure phases that only occurred at elevated temperatures, this phase transition occurs at the lowest temperatures investigated, \ensuremath{\sim}5 K, and the steep phase line indicates that it is a quantum phase transition. This phase is characterized by two distinct IR absorption bands (2950 and $3335\phantom{\rule{0.16em}{0ex}}\mathrm{c}{\mathrm{m}}^{\ensuremath{-}1}$ at 365 GPa). Above the transition pressure we observe strong darkening of the sample in the visible spectrum as pressure is increased. Observations are compatible with the cmca-12 crystal structure.

Detecting Superconductivity in the High Pressure Hydrides and Metallic Hydrogen from Optical Properties

We present a new technique for measuring the critical temperature T_{c} in the high pressure, high T_{c} electron-phonon-driven superconducting hydrides. This technique does not require connecting leads to the sample. In the region of the absorption spectrum above the sum of the optical gap and maximum phonon energy, the reflectance mirrors the temperature variation of the superconducting order parameter. For an appropriately chosen value of fixed photon energy, the temperature dependence of the reflectance varies much more rapidly below T=T_{c} than above. It increases with increasing temperature in the superconducting state while it decreases in the normal state. Examining the temperature dependence of the reflectance at a fixed photon energy, there is a cusp at T=T_{c} which provides a measurement of the critical temperature. We discuss these issues within the context of the recently reported atomic metallic phase of hydrogen, but our proposed technique should prove useful for other hydrides with large coupling to high energy phonons.

Metallic atomic hydrogen at a pressure of 300-500 GPa

Atomic metallic hydrogen with a symmetry FDDD of a lattice cell is shown to have a stable crystalline structure under hydrostatic compression in the pressure range of 350-500 GPa. The resulting phase is shown to have a stable structure regarding the collapse of the phonon spectrum. Ab-initio simulation method has been used to calculate the structural, electronic, phonon and other characteristics of the normal FDDD metallic phase of hydrogen at a pressure of 350-500 GPA.

Reconstruction of bands in metallic hydrogen

The generalized theory of normal properties of a metal for the case of the properties of the electronic band of electron–phonon systems with a variable electron density of states is used to study the normal phase of metallic hydrogen at a pressure of 500 GPa and a temperature of 200 K. We calculated the frequency dependence of the real ReΣ(ω) and imaginary ImΣ(ω) parts of the self-energy part of the electron Green’s function Σ(ω), as well as the electron density of states N(e) of the stable phase of metallic hydrogen with the I41/amd symmetry at a pressure of 500 GPa, renormalized by the strong electron–phonon coupling. It is found that the electron conduction band of the I41/amd phase of metallic hydrogen undergoes insignificant reconstruction near the Fermi level because of the renormalization by the electron–phonon coupling.

Critical temperature of metallic hydrogen at a pressure of 500 GPa

The Eliashberg theory generalized for electron–phonon systems with a variable electron density of states is used to study Tc in the I41/AMD phase of metallic hydrogen under compression taking into account the frequency behavior of the renormalization of the mass of the electron and the chemical potential. The phonon contribution to the anomalous electron Green’s function is considered. Pairing is taken into account within the entire electron band rather than in a narrow region near the Fermi surface. The frequency and temperature dependences of the complex renormalization of the mass Re Z(ω), as well as the density of states N(ω) renormalized by the electron–phonon coupling and the spectral function of the electron–phonon coupling, which are obtained in calculations, are used to calculate the anomalous electron Green’s function. The frequency dependence of the real and imaginary parts of the order parameter in the I41/AMD phase is obtained. The solution of the system of Eliashberg equations gives the value Tc = 217 K in the I41/AMD phase of hydrogen at a pressure of 500 GPa.

Electron-phonon interaction and superconductivity in metallic molecular hydrogen. II. Superconductivity under pressure

A detailed study of the electron-phonon interaction in the $Cmca$ phase of metallic hydrogen and of its implications in the superconducting properties is presented. A careful analysis of the role played by anisotropy and by the presence of superconducting multigaps allows to single out the peculiarities that drive superconductivity at very high temperature in this system.

A note on the metallization of compressed liquid hydrogen

We examine the molecular-atomic transition in liquid hydrogen as it relates to metallization. Pair potentials are obtained from first principles molecular dynamics and compared with potentials derived from quadratic response. The results provide insight into the nature of covalent bonding under extreme conditions. Based on this analysis, we construct a schematic dissociation-metallization phase diagram and suggest experimental approaches that should significantly reduce the pressures necessary for the realization of the elusive metallic phase of hydrogen.

High temperature equation of state of metallic hydrogen

The equation of state of liquid metallic hydrogen is solved numerically. Investigations are carried out at temperatures from 3000 to 20 000 K and densities from 0.2 to 3 mol/cm3, which correspond both to the experimental conditions under which metallic hydrogen is produced on earth and the conditions in the cores of giant planets of the solar system such as Jupiter and Saturn. It is assumed that hydrogen is in an atomic state and all its electrons are collectivized. Perturbation theory in the electron-proton interaction is applied to determine the thermodynamic potentials of metallic hydrogen. The electron subsystem is considered in the randomphase approximation with regard to the exchange interaction and the correlation of electrons in the local-field approximation. The proton-proton interaction is taken into account in the hard-spheres approximation. The thermodynamic characteristics of metallic hydrogen are calculated with regard to the zero-, second-, and third-order perturbation theory terms. The third-order term proves to be rather essential at moderately high temperatures and densities, although it is much smaller than the second-order term. The thermodynamic potentials of metallic hydrogen are monotonically increasing functions of density and temperature. The values of pressure for the temperatures and pressures that are characteristic of the conditions under which metallic hydrogen is produced on earth coincide with the corresponding values reported by the discoverers of metallic hydrogen to a high degree of accuracy. The temperature and density ranges are found in which there exists a liquid phase of metallic hydrogen.

Charge transfer in hydrogen

Possible charge transfers in a single hydrogen molecule are discussed in connection with the energetic sequence and relation to transitions in high-pressure solid hydrogen. Transition pressure to atomic metallic hydrogen was estimated to about 8±1 Mbar, based on recent evaluation of the free energy of molecular hydrogen and the equation of state for the atomic metallic phase of hydrogen by Kagan et al. (Zh. Eksp. Teor. Fiz. 73 (1977) 967). The size of the H − ion as a function of pressure is discussed and a possible stepwise (quantized) ionization of the H 2 species in high pressures is formulated. The possibility of solution formation of covalent and ionic hydrogens is mentioned, and an example of a transition from covalent to ionic bond is given.

Density-functional theory of pair correlations in metallic hydrogen

The pair correlations in the metallic phase of hydrogen are reconsidered on the basis of a simple density-functional formulation of the free energy of the ion-electron plasma, which includes a square-gradient correction to the Thomas-Fermi kinetic energy of the degenerate electrons. A robust prescription is given for the prefactor of the square-gradient correction. The functional leads to a hypernetted-chain--like closure for the ion-ion and ion-electron correlation functions, which is solved iteratively, in conjunction with the coupled Ornstein-Zernike equations relating the matrices of pair and direct correlation functions. The resulting structure agrees well with available ab initio simulation data based on the Kohn-Sham functional. A density- and temperature-dependent effective ion-ion pair potential is obtained by formally reducing the initial two-component system to a one-component fluid of pseudoatoms. The results show strong deviations of the present nonlinear theory from the standard linear screening approach for ${r}_{s}>1$ (where ${r}_{s}$ is the usual inverse density parameter equal to the ratio of the electron sphere radius over the Bohr radius). The long-wavelength ion density fluctuations are strongly enhanced as the density drops, and at the lowest density ${(r}_{s}=1.5)$ the ion-ion pair structure and effective potential exhibit an unusual behavior, at the lower temperature explored in this paper $(T=3\ifmmode\times\else\texttimes\fi{}{10}^{3}\mathrm{K}),$ which may be interpreted as a precursor to an incipient plasma-insulator transition. Thermodynamic properties are estimated from the pair structure. The influence of nonlinear electron polarization on the equation of state is found to be surprisingly small, but the isothermal compressibility increases sharply at the lowest density.

Theoretical study of atomic phases of metallic hydrogen.

Several structures are considered as candidates for the predicted high-pressure (above 400 GPa) atomic phase of metallic hydrogen. Results for the cubic phases are found to agree well with previous calculations. Two particularly interesting structures are the primitive hexagonal (ph) and rhombohedral (9R), which are found to be particularly stable and may be good candidates for the structure of atomic metallic hydrogen.

Crystal-liquid transition in metallic hydrogen

Using the functional approach to the theory of crystals, we show that, with an increase in pressure, the zero-point vibrations of the crystal lattice break it down. From comparison of the pressure functionals for the crystalline and liquid phase of metallic hydrogen, we obtain a lower estimate for the critical density in the low-temperature limit.

Chemical potentials in dense charged classical or quantal systems.

We report a general method for evaluating the partial chemical potentials of a dense neutral multicomponent system of charged particles. The results of this analysis can be directly applied to the evaluation of chemical potentials and partial chemical potentials for the electron gas, for a neutral two-component charged system such as the metallic phase of hydrogen, and even for a three-component system such as a metal hydride.

Ordered pairing in liquid metallic hydrogen

We study two possible types of pairing involving the protons of a proposed low-temperature liquid phase of metallic hydrogen. Electron-proton pairing, which can result in an insulating phase, is investigated by using an approximate solution of an Eliashberg-type equation for the anomalous self-energy. A very low estimate of the transition temperature is obtained by including proton correlations in the effective interaction. For proton-proton pairing, we derive a new proton pair potential based on the Abrikosov wave function. This potential includes the electron-proton interaction to all orders and has a much larger well depth than is obtained with linear screening methods. This suggests the possibility of either a superfluid paired phase analogous to that in ${\mathrm{He}}^{3}$, or alternatively a phase with true molecular pairing.

Two-component Fermi-liquid theory: Transport properties of liquid metallic hydrogen

We have examined the elementary transport properties of a two-charged-component normal Fermi liquid using a generalized Landau-Silin-Boltzmann-equation approach. ''Exact'' expressions involving the phenomenologically treated quasiparticle scattering amplitudes are given for the low-temperature electrical and thermal conductivities, viscosity, and spin-diffusion constants. The results are applied to the case of a possible low-temperature normal liquid metallic phase of hydrogen, i.e., interpenetrating electron and proton fluids. We find the thermal and electrical conductivities and electron-spin-diffusion constant to be vastly smaller (by roughly a factor of the square of the electron-to-proton mass ratio) in a normal liquid than in a normal solid metallic phase of hydrogen of comparable density. We also discuss the collective modes in the collisionless regime.

Low-temperature thermostatics of face-centered-cubic metallic hydrogen

The thermostatic properties of a high-symmetry phase of metallic hydrogen with atomic sphere radius between 0.1 and 1.5 bohr are studied, with special emphasis accorded to electronic screening and quantum proton motion. The electron-proton and proton-proton interactions receive a perturbation treatment based on the Singwi dielectric function, while the proton motion is handled by self-consistent harmonic approximation. Quantum behavior is found to be less pronounced than expected, and nuclear magnetism is absent. The phonon spectrum is, however, affected by screening and large proton motion. The zero-point vibrational energy and the superconducting critical temperature are below previous estimates. The crystalline-defect formation energies are a few times the Debye energy, which implies that defects contribute significantly to melting at the lower particle densities.

Metallic hydrogen II high-temperature superconductivity

In this paper we discuss the possibility and the consequences of high-temperature superconductivity in the proposed metallic phase of hydrogen. Using the results of an earlier paper we also consider the pressure dependence and the connection of high-temperature superconductivity with metallic hydrogen properties.

Zenomagnetic core-mantle coupling and the rotation of Jupiter's Great Red Spot

Fluctuations of the order of several seconds in the period of rotation of Jupiter's Great Red Spot have been observed by Reese and Solberg (1966) to occur within intervals of not more than a few months. On Hide's (1961) hypothesis that the Red Spot is a persistent feature attached to the solid surface of the planet, these fluctuations may indicate an internal redistribution of Jupiter's angular momentum. Evidence for a strong zenomagnetic field and for a transition from the molecular to the metallic phase of hydrogen at pressures of a few Mb have led Gallet (1961) and Runcorn (1967) to suggest that angular momentum may be transferred between the solid molecular hydrogen mantle and a liquid metallic core. Adopting their model for Jupiter's interior and using the theory of electromagnetic coupling which has successfully explained the irregular changes in the Earth's rotation period, the electrical conductivity of the Jovian mantle can be estimated. The result is not inconsistent with such slight evidence as exists for changes in the rotation period of the decametre radio sources.