N. W. Ashcroft

Electron-ion pseudopotentials in metals☆

Abstract Pseudopotential form-factors for Al, Pb, Na and K are plotted for a simple model potential which is justified in the text. They are in good agreement with potentials of Heine and Abarenkov.

Pairing in dense lithium

The light alkali metals have played an important role in the developing understanding of the electronic structure of simple metals. These systems are commonly viewed in terms of an underlying interacting electron gas permeated by periodic arrays of ions normally occupying only a small fraction of the crystal volume. The electron–ion interaction, or equivalently the pseudopotential, has been argued to be weak in such systems, reflecting the partial cancellation of nuclear attraction by the largely repulsive effects of Pauli exclusion by the core electrons. Current experiments can now achieve densities at which the core electrons substantially overlap, significantly reducing the fractional volume available to fixed numbers of valence electrons. Here we report the results of first-principles calculations, indicating that lithium, the band structure of which is largely free-electron-like at ordinary densities, does not follow the intuitive expectations of quantum mechanics by becoming even more free-electron-like at higher densities. Instead, at high pressure its electronic structure departs radically from nearly free-electron behaviour, and its common symmetric structure (body-centred cubic, b.c.c.) becomes unstable to a pairing of the ions. Once paired, lithium possesses an even number of electrons per primitive cell which, although not sufficient, is at least necessary for insulating (or semiconducting) behaviour within one-electron band theory.

A little bit of lithium does a lot for hydrogen

From detailed assessments of electronic structure, we find that a combination of significantly quantal elements, six of seven atoms being hydrogen, becomes a stable metal at a pressure approximately 1/4 of that required to metalize pure hydrogen itself. The system, LiH6 (and other LiHn), may well have extensions beyond the constituent lithium. These hypothetical materials demonstrate that nontraditional stoichiometries can considerably expand the view of chemical combination under moderate pressure.

A superconductor to superfluid phase transition in liquid metallic hydrogen

Although hydrogen is the simplest of atoms, it does not form the simplest of solids or liquids. Quantum effects in these phases are considerable (a consequence of the light proton mass) and they have a demonstrable and often puzzling influence on many physical properties, including spatial order. To date, the structure of dense hydrogen remains experimentally elusive. Recent studies of the melting curve of hydrogen indicate that at high (but experimentally accessible) pressures, compressed hydrogen will adopt a liquid state, even at low temperatures. In reaching this phase, hydrogen is also projected to pass through an insulator-to-metal transition. This raises the possibility of new state of matter: a near ground-state liquid metal, and its ordered states in the quantum domain. Ordered quantum fluids are traditionally categorized as superconductors or superfluids; these respective systems feature dissipationless electrical currents or mass flow. Here we report a topological analysis of the projected phase of liquid metallic hydrogen, finding that it may represent a new type of ordered quantum fluid. Specifically, we show that liquid metallic hydrogen cannot be categorized exclusively as a superconductor or superfluid. We predict that, in the presence of a magnetic field, liquid metallic hydrogen will exhibit several phase transitions to ordered states, ranging from superconductors to superfluids.

The Revealing Role of Pressure in the Condensed Matter Sciences

Matter in bulk has both a microscopic and macroscopic description, with the latter going back to the very earliest days of thermodynamics. Of the common thermodynamic variables pressure (p) and temperature (T), it is temperature that has played by far the most prominent role in probing condensed matter and in our fundamental understanding of it. However, even as far back as 1660, Robert Boyle declared in his famous treatise commonly known as Touching the Spring of the Air that “perhaps the pressure of the air might have an interest in more phenomena than men have hitherto thought.” More than three centuries later, we can see how right he was, as systematic use of pressure has led to considerable insight into the properties of matter, especially its electronic properties. As A. Jayaraman noted when he was at ATT...

Theory of the Thermodynamics of Simple Liquid Metals

Publisher Summary The chapter presents a discussion on the thermodynamic properties of conducting liquids. The chapter discusses calculating measurable quantities as the compressibility, specific heat, and melting curves of metals from knowledge of the fundamental interactions among the electrons and ions. To understand this problem, it is necessary to consider both the electronic structure and the “bonding” structure or ionic arrangement. These are closely interrelated. For example, any description of the ionic arrangement must take into account the presence of the conduction electrons. Conversely, the electronic structure must in turn be strongly affected by the physical arrangement of the ions. The interplay between these dual aspects of liquid metals is quite complex, which is discussed in this chapter. Liquid metals may be further divided into roughly nonoverlapping classes according to their electronic structure, the chapter defines these classes under normal condition. A central question regarding liquid metals is, of course, why they form simple liquids, or equivalently, why, structurally, they have two body-central forces. The answer, in the case of free-electron metals, lies in the predictions of perturbation theory as applied to an interacting electron gas. The perturbation arises from the metallic ions which carry with them, in an adiabatic way, the fundamental interaction between the electrons and ions—the pseudopotential. The response of the electrons to this perturbation is discussed in the chapter. Once the nature of the interatomic forces is known, the thermodynamics of the liquid metal can be determined by the methods of classical statistical mechanics. Some of the methods for so doing are discussed in this chapter.

Structure and bandgap closure in dense hydrogen

The possibility that steadily compressed hydrogen might undergo a transition from a proton-paired insulator to a monatomic metal was first suggested in 1935 (ref. 1). But experimental realization of metallic hydrogen in solid form has remained elusive, despite studies at pressures as high as 342 GPa (ref. 2). The pairing structure is known to be robust (from the persistence of its associated vibron mode), leading to the suggestion of an alternative route to the metallic state, involving a band-overlap transition in which the pairing is preserved. Here we report density functional calculations within the local density approximation that predict a range of densities for hydrogen where a paired or molecular metallic state may be energetically preferred. The transition to this metallic state is naturally associated with the closing of an overall bandgap; but the pressures required to effect the transition are shown to change significantly when the gaps are corrected by approximate inclusion of many-electron effects. The implication is that a complete resolution of the structural and phase problem in dense hydrogen may require methods beyond the local density approximation.

Electron-ion pseudopotentials in the alkali metals

Through the choice of a single parameter (an effective core radius Rcore) a simple model potential for the electron-ion interaction in a metal yields form factors V(K) similar to those of the Heine-Abarenkov model potentials. Values of Rcore near to the usual ionic radii give V(K) curves which are shown to be useful for momentum transfers K in the transport range and nearby, the region of interest normally encountered in the theory of metals. The potentials are applied in the calculation of resistivities, phonon spectra and phase shifts. Energy-dependent properties of the potentials are inferred from thermopower data.

On the constitution of sodium at higher densities.

Using density functional theory the atomic and electronic structures of sodium are predicted to depart substantially from those expected of simple metals for r(s)<2.48 ( p>130 GPa). Newly predicted phases include those with low structural symmetry and semimetallic electronic properties (including zero-gap semiconducting limiting behavior), and even those that raise the possibility of superconductivity, all at currently achievable pressures. Important differences emerge between sodium and lithium at high densities, and these are attributable to corresponding differences in their respective cores.

Benzene under high pressure: A story of molecular crystals transforming to saturated networks, with a possible intermediate metallic phase

In a theoretical study, benzene is compressed up to 300 GPa. The transformations found between molecular phases generally match the experimental findings in the moderate pressure regime (<20 GPa): phase I (Pbca) is found to be stable up to 4 GPa, while phase II (P4(3)2(1)2) is preferred in a narrow pressure range of 4-7 GPa. Phase III (P2(1)/c) is at lowest enthalpy at higher pressures. Above 50 GPa, phase V (P2(1) at 0 GPa; P2(1)/c at high pressure) comes into play, slightly more stable than phase III in the range of 50-80 GP, but unstable to rearrangement to a saturated, four-coordinate (at C), one-dimensional polymer. Actually, throughout the entire pressure range, crystals of graphane possess lower enthalpy than molecular benzene structures; a simple thermochemical argument is given for why this is so. In several of the benzene phases there nevertheless are substantial barriers to rearranging the molecules to a saturated polymer, especially at low temperatures. Even at room temperature these barriers should allow one to study the effect of pressure on the metastable molecular phases. Molecular phase III (P2(1)/c) is one such; it remains metastable to higher pressures up to ∼200 GPa, at which point it too rearranges spontaneously to a saturated, tetracoordinate CH polymer. At 300 K the isomerization transition occurs at a lower pressure. Nevertheless, there may be a narrow region of pressure, between P = 180 and 200 GPa, where one could find a metallic, molecular benzene state. We explore several lower dimensional models for such a metallic benzene. We also probe the possible first steps in a localized, nucleated benzene polymerization by studying the dimerization of benzene molecules. Several new (C(6)H(6))(2) dimers are predicted.