| dc.description.abstract | Hydrogen is the only atom for which the Schr odinger equation is solvable. Consisting
only of a proton and an electron, hydrogen is the lightest element and, nevertheless, is
far from being simple. Under ambient conditions, it forms diatomic molecules H2 in gas
phase, but di erent temperature and pressures lead to a complex phase diagram, which
is not completely known yet. Solid hydrogen was rst documented in 1899 [1] and was
found to be isolating. At higher pressures, however, hydrogen can be metallized. In 1935
Wigner and Huntington predicted that the metallization pressure would be 25 GPa [2],
where molecules would disociate to form a monoatomic metal, as alkali metals that lie
below hydrogen in the periodic table. The prediction of the metallization pressure turned
out to be wrong: metallic hydrogen has not been found yet, even under a pressure as
high as 320 GPa. Nevertheless, extrapolations based on optical measurements suggest
that a metallic phase may be attained at 450 GPa [3].
The interest of material scientist in metallic hydrogen can be attributed, at least to a
great extent, to Ashcroft, who in 1968 suggested that such a system could be a hightemperature
superconductor [4]. The temperature at which this material would exhibit a
transition from a superconducting to a non-superconducting state (Tc) was estimated to
be around room temperature. The implications of such a statement are very interesting
in the eld of astrophysics: in planets that contain a big quantity of hydrogen and
whose temperature is below Tc, superconducting hydrogen may be found, specially at the
center, where the gravitational pressure is high. This might be the case of Jupiter, whose
proportion of hydrogen is about 90%. There are also speculations suggesting that the
high magnetic eld of Jupiter is due to persistent currents related to the superconducting
phase [5]. Metallization and superconductivity of hydrogen has puzzled scientists for
decades, and the community is trying to answer several questions. For instance, what
is the structure of hydrogen at very high pressures? Or a more general one: what is the
maximum Tc a phonon-mediated superconductor can have [6]?
A great experimental e ort has been carried out pursuing metallic hydrogen and trying
to answer the questions above; however, the characterization of solid phases of hydrogen
is a hard task. Achieving the high pressures needed to get the sought phases requires
advanced technologies. Diamond anvil cells (DAC) are commonly used devices. These
devices consist of two diamonds with a tip of small area; for this reason, when a force is applied, the pressure exerted is very big. This pressure is uniaxial, but it can be turned
into hydrostatic pressure using transmitting media. Nowadays, this method makes it
possible to reach pressures higher than 300 GPa, but even at this pressure hydrogen does
not show metallic properties. A recently developed technique that is an improvement
of DAC can reach pressures as high as 600 GPa [7], so it is a promising step forward in
high pressure physics. Another drawback is that the electronic density of the structures
is so low that X-ray di raction patterns have low resolution. For these reasons, ab
initio studies are an important source of knowledge in this eld, within their limitations.
When treating hydrogen, there are many subtleties in the calculations: as the atoms
are so light, the ions forming the crystalline lattice have signi cant displacements even
when temperatures are very low, and even at T=0 K, due to Heisenberg's uncertainty
principle. Thus, the energy corresponding to this zero-point (ZP) motion is signi cant
and has to be included in an accurate determination of the most stable phase. This has
been done including ZP vibrational energies within the harmonic approximation for a
range of pressures and at T=0 K, giving rise to a series of structures that are stable in
their respective pressure ranges [8]. Very recently, a treatment of the phases of hydrogen
that includes anharmonicity in ZP energies has suggested that relative stability of the
phases may change with respect to the calculations within the harmonic approximation
[9].
Many of the proposed structures for solid hydrogen have been investigated. Particularly,
the Cmca-4 structure, which was found to be the stable one from 385-490 GPa [8], is
metallic. Calculations for this structure, within the harmonic approximation for the
ionic motion, predict a Tc up to 242 K at 450 GPa [10]. Nonetheless, due to the big
ionic displacements, the harmonic approximation may not su ce to describe correctly
the system. The aim of this work is to apply a recently developed method to treat
anharmonicity, the stochastic self-consistent harmonic approximation (SSCHA) [11], to
Cmca-4 metallic hydrogen. This way, we will be able to study the e ects of anharmonicity
in the phonon spectrum and to try to understand the changes it may provoque in
the value of Tc.
The work is structured as follows. First we present the theoretical basis of the calculations:
Density Functional Theory (DFT) for the electronic calculations, phonons in the
harmonic approximation and the SSCHA. Then we apply these methods to Cmca-4 hydrogen
and we discuss the results obtained. In the last chapter we draw some conclusions
and propose possible future work. | es |
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