To the editors:
The most important ingredient in most molecules is the covalent bond that holds atoms together. Covalent bonding comprises electrons shared between the two atoms. Electrons seek to lower their energy, and in covalent bonds the negatively charged electrons can lower their energy by associating themselves with two positively charged ions, rather than a single atom.
Under pressure, solid materials obey a second imperative: as well as lowering energy, they seek to reduce their volume. Materials can do this by spreading their electrons throughout space: in quantum mechanics the electron is able to be everywhere at once. This esoteric notion gives rise to a familiar state of matter: metals.
It is believed that under sufficient pressure, all elements will become metallic. In the early days of quantum mechanics, Eugene Wigner and Hillard Huntington accurately calculated the density at which the electrons in hydrogen would be expelled from the covalent bond, forming an atomic metal.1 The quantum theory of 1935 did not allow them to calculate the pressure required, but their paper contains a handwaving estimate of 35 gigapascals (GPa), based on the wrong assumption that dense hydrogen would compress as easily as molecular hydrogen.
In 1935, 35GPa was an incomprehensibly large pressure. Today, it is routinely obtained by an ingenious device known as a diamond anvil cell. This device comprises a sample trapped between two opposed diamonds; pressure is applied to the sample by moving the diamonds together. By concentrating a modest force onto a tiny sample, huge pressures can be obtained. Unfortunately, 35GPa proved insufficient to reach the densities needed to metalize hydrogen. Modern quantum mechanical calculations suggested at least an order of magnitude higher would be needed. Rival groups around the world battled to be the first to reach the necessary pressure.
The high-pressure physicists were not alone in the search for metallic hydrogen. Even before 1935, atomic hydrogen was known as a component of metallic alloys.2 In the 1950s, it became known that fusion bombs and reactors could strip the electrons from hydrogen with temperature alone, albeit at millions of kelvins, producing a plasma state few would regard as metallic. In 1973, the Pioneer 10 spacecraft sent back measurements from Jupiter, showing an astonishingly large magnetic field. The only plausible cause was a dynamo created by a giant spinning core of metallic hydrogen.3 Metallic hydrogen was created by the gravitational force of the entire planet. Then, back on Earth in 1996, scientists at Lawrence Livermore weapons laboratory reported that fluid hydrogen became metallic at 140GPa and 3,000K.4 This was well below the expected density, implying that both temperature and pressure were contributing to breaking the bonds. Static experiments up to 2,200K showed similar metallization, with a strong isotope dependence showing that the nuclei still behave in a quantum fashion. It is a matter of definition rather than measurement as to whether this is pressure-driven metallization or a temperature-driven plasma transition.
Experimental observation of hydrogen before 2017 showed that the bandgap was closing, but hydrogen remained a molecular non-metal up to 340GPa.5 It is worth mentioning that both theory and experiment have wide uncertainties in the measurement of pressure in the International System of Units, so identifying the actual pressures obtained can be controversial. The apparent conflict between transparent hydrogen at 342GPa and black hydrogen at 320GPa is likely to come from pressure measurement.6 Furthermore, temperature effects are significant: room-temperature conductivity occurs at much lower pressures than at liquid nitrogen temperatures, consistent with the shock-wave result that increased temperature facilitates conduction. While these seminal papers were initially open to criticism for lack of reproducibility, repeated studies by independent teams leave little doubt of their veracity. Hundreds of diamonds have been shattered in pressure cells around the world to produce consensus that the lowest pressure solid metallic hydrogen is molecular.
By 2000, theoretical methods for calculating the crystal structure finally became available, and a surprising new idea emerged: molecular metallic hydrogen.7 Rather than breaking into individual atoms, the hydrogen molecules became stretched under pressure, to the point where electrons could flow between them.8 The atomic phase was predicted to have an open structure with each hydrogen bonded to only four others. This resembles the high-pressure structures of the alkali metals, which lie below hydrogen in the periodic table, rather than the densely packed structure seen in these elements under normal conditions and assumed by Wigner and Huntington.
In their controversial 2017 paper, Rangas Dias and Isaac Silvera reported the transition to atomic hydrogen.9 Consistent with previous studies, their sample went first through the opaque phase and then, at 495GPa, into a reflecting phase with properties resembling the theoretically predicted fourfold coordinated atomic hydrogen phase. The credibility of the paper was damaged by some speculation concerning rocket propellant and energy transmission, but these mentions are likely to be a nod to their funders and are irrelevant to the actual experiment.10 A more serious criticism is that they failed to characterize the sample with spectroscopic measurements. This highlights a fundamental dilemma that researchers face: spectroscopy requires shining a laser, which runs a risk of destroying the diamonds and the sample if it becomes a good energy absorber—that is, a metal. More recent claims of metallic hydrogen from Mikhail Eremets’s and Paul Loubeyre’s groups are consistent with one another, suggesting a sharp increase in reflectivity at 425GPa.11 Loubeyre et al. attempted spectroscopy at the highest pressures, but were unable to obtain a convincing signal consistent with having a good metal.
These measurements are often taken at low temperatures because diamonds are less likely to break. At room temperature, metallization is expected to occur at lower pressures. Using Raman work, up to 325GPa, the Eugene Gregoryanz group found three molecular phases, none of which were metallic.12 An X-ray study by Ho-Kwang Mao’s group reached 254GPa at room temperature.13 Consistent with these molecular phases, they reported an “isostructural electronic transition”—something possible only in a metal—but no experimental evidence of metallicity was presented and more detailed analysis found no electronic transition in theory either.14
Solid hydrogen is often referred to as a quantum solid—normally without any definition of what that means. Since all materials behave in accordance with the laws of quantum mechanics, and spectroscopy would be impossible without quantization of electronic levels, the term quantum-solid cannot be incorrect. Neglecting quantum mechanics can introduce errors of up to 100GPa in pressure calculations.15 A more useful measure of a quantum solid is whether its different isotopes, hydrogen and deuterium, behave differently—this is true at low temperatures and pressures at which solid hydrogen has the remarkable quantum property that the molecules point in all directions at once, yet do not rotate. Such isotope effects also affect metallization in the liquid phase.16
Despite the controversies, misleading paper titles, and discrepancies in reported pressures, the general picture is consistent across all groups and between experiment and theory. One cannot expect studies at different temperatures to yield identical transition pressures. Pressure measurement itself is not straightforward: different groups use different indicators of pressure. The scales used by Loubeyre’s group, for example, give values lower than other groups by many tens of gigapascals. Theoretical pressure calculation is also highly sensitive to methodology.17 Thus a discrepancy in reported pressure between studies is not evidence of a problem with other measurements.
In the last few years the focus has switched from conducting hydrogen to superconducting hydrogen.18 Conductivity in a metal is reduced when the electrons moving through the material are knocked off-course, or scattered, either by impurities or moving atoms. In a superconductor, all the electrons are connected together, so an obstacle that might scatter one electron is unable to affect them all at once. The connections are provided by a quantum effect mediated by the atoms, and light atoms provide the strongest connections, able to withstand the highest temperature. Thus solid atomic hydrogen is expected to be a high temperature superconductor, probably above room temperature.19 Metallic atomic hydrogen in alloys was observed experimentally even before Wigner and Huntington, and since the 1970s, it has been known to enhance superconductivity.20 Much recent work has concentrated on finding hydrogen-rich compounds that preserve the superconducting properties of atomic hydrogen. The breakthrough experiment in this area was the 2015 discovery of superconductivity in hydrogen sulfide21—a material believed to have chemical composition H3S, unlike the H2S one expects from chemical bonding. Since then, numerous other materials have been produced with superconducting temperatures around 200K. Quantum theoretical calculation of these materials requires some strong approximations, but is typically accurate to within tens of kelvins, and a similar uncertainty is seen in reproducing the experiments.22 By 2019, Eremets’s group had increased their record to 250K in a lanthanum hydride: a material whose superconductivity has been tested for over fifty years.23 The exact composition cannot be determined, but theoretical work suggests that LaH10, with cages of atomic hydrogen confining each lanthanum, is the likely structure. The superconductivity is primarily within the connected network of hydrogens, while the breaking of the covalent bonds is facilitated by electrons released by the La ions.
The goal of room temperature superconductivity was now in sight, and the first report of this came this year from Dias’s group in Rochester.24 This was for a material made from H2S and methane, although at pressures at which the covalent bonds will be broken. Unlike other hydrogen-rich superconductors, there is no theoretical explanation for this effect, and like Dias’s work on metallic hydrogen, this experiment still awaits independent reproduction.
Wigner and Huntington calculated the properties of high-density, low temperature, body-centered cubic, metallic hydrogen. Nobody has claimed to observe this precise material. Whether the predictions in their 1935 paper “On the Possibility of a Metallic Modification of Hydrogen” have been realized has become a matter of definition. Atomic hydrogen was already a known component of metallic alloys at that time. Metallic fluid pure hydrogen exists permanently in planets and was made fleeting on Earth during shock waves. Long-lived conducting molecular hydrogen has been made repeatedly in diamond anvil cells by many groups over the past twenty years. To date, pure solid atomic hydrogen was only reported by Dias and Silvera. Superconducting solid hydrogen has been observed, but only in compounds in which cations donate electrons to assist breaking the molecules. Nobody has observed hydrogen in the closely packed structures adopted by the alkali metal elements and taken as a model by Wigner and Huntington.
Huntington died in 1993, and Wigner in 1995. We will never know which, if any, of these remarkable discoveries they would regard as proof of their predictions.
Graeme Ackland
Isaac Silvera & Ranga Dias reply:
Graeme Ackland has written a long letter in response to our review. For many years, Ackland has substantially contributed to the theoretical understanding of hydrogen and its isotopes. In his letter, he provides his point of view, but some of his comments raise strong reactions in us. We shall respond, more or less in the sequential order of his comments. Some of our responses are corrections, some are our point of view, and some point out instances in which he does not appear to have carefully read the literature.
First, Ackland states that Eugene Wigner and Hillard Huntington predicted the metallization pressure to be 35GPa (100GPa = 1 megabar). Wigner and Huntington clearly state a value of 250,000 atmospheres, which is 25.3GPa, not 35GPa.25
It is now well known both theoretically and experimentally that there are two pathways to metallic hydrogen: the low-temperature pathway of Wigner and Huntington and the high-temperature pathway that is a first-order phase transition from insulating liquid molecular hydrogen to liquid atomic hydrogen. This latter is known as a liquid–liquid phase transition or, sometimes, the plasma phase transition.26 This phase transition has a pressure–temperature phase line and has been experimentally observed for hydrogen and deuterium.27 The Livermore group, due to their thermodynamic pathway, did not observe the phase transition line.28 But the transition is well understood. For certain values of pressure and temperature above the melting line, the sample is in an insulating liquid molecular phase; as pressure increases at a given temperature, the sample transforms to liquid atomic metallic hydrogen. It is this form of metallic hydrogen that makes up most of the core of Jupiter. Ackland wrongly implies that this pressure–temperature region is vaguely understood when he writes, “It is a matter of definition rather than measurement as to whether this is pressure-driven metallization or a temperature-driven plasma transition.”
Ackland then states that there are wide uncertainties when determining pressure in hydrogen that can explain the inconsistent observations of independent research groups. Experimentalists use the shift of a vibron peak in hydrogen up to a pressure of about 350GPa. For higher pressures, in the past decade, the community has adopted the shift of the Raman active phonon in the stressed part of the diamond anvils. This method has a systematic uncertainty of about ±13GPa in the ultra-high pressure region.29 Neither of these scales explains why Loubeyre’s group sees hydrogen becoming black at 320GPa, where almost all other groups observe it to be transparent, or why their pressures differ by more than 13GPa from those reported by others.30 Moreover, a given group usually generates pressure measurements that are consistent based on their methods and calibration, but the Loubeyre group has reported black hydrogen at 300, 310, and 320GPa. This might imply problems with their sample.
“Hundreds of diamonds,” Ackland remarks, “have been shattered in pressure cells around the world to produce consensus that the lowest pressure solid metallic hydrogen is molecular.” At this time, there is no consensus on this subject. Instead, the discussion is focused on two papers. One claim is made by the Loubeyre group, who had no direct measurement of molecular metallic hydrogen.31 Their claim was instead based on results from Mikhail Eremets’s group. In an expanded article, we have shown that the claim by the Eremets group is questionable.32
Ackland goes on to state that our observation of the Wigner–Huntington form of metallic hydrogen is controversial. The metallic hydrogen hunters include a contentious group of wannabe researchers among their ranks. When we published our paper, this group criticized several aspects of our work.33 We have published a detailed response to their claims on arXiv.34
Based on their experience, Xiao-Di Liu et al., of the Eugene Gregoryanz group, do not believe our achieved pressure of 495GPa.35 They state that out of their 120 experimental runs, only five exceeded 350GPa—that is, they suffered a 96% failure rate. In each run, they used the same procedure, and one might well expect the same result, failure. In our paper, we present the techniques we used to achieve the higher pressure, including use of synthetic diamonds, coating the diamonds with alumina as a hydrogen diffusion barrier, and cryogenic loading.36 We have had an almost 100% success rate in reaching high pressures. Our main problem is in cryogenic loading; sometimes the sample is not confined in the gasket hole, and it closes under load. We do not count these as failures to reach high pressure. Several other reviewers have commented on the pressure in these experiences, suggesting that nobody has achieved such high pressures with conventional diamond anvils. These reviewers appear not to read the literature, which reports that 560GPa was achieved thirty years ago using conventional diamonds.37 In short, there were a litany of questions and criticisms about our work that were easily dealt with.
We showed that the sample was metallic by measuring the wavelength and temperature dependence of its reflectance to show that it was a conductor with a single electron per atom, or atomic metallic hydrogen. No one objected to this physics. The only important suggestions that we received were that the experiment should be reproduced and that short wavelength reflectance measurements of metallic hydrogen should not be included due to absorption of light by the diamond in this region. Thus, our observation of metallic hydrogen is not scientifically controversial. Ackland should have carefully read other reviews and our responses before suggesting so.
Ackland refers to an earlier complaint that our discussion of metallic hydrogen as a possible rocket propellant damages the credibility of the achievement. On the contrary, we believe that it is important to discuss possible applications of fundamental research to society; the public is always interested in applications, as are funders.
Curiously, Ackland states, “A more serious criticism is that they failed to characterize the sample with spectroscopic measurements.” Measurement of the wavelength dependance of reflectance is a spectroscopic measurement. He goes on: “More recent claims of [molecular] metallic hydrogen from Mikhail Eremets’s and Paul Loubeyre’s groups are consistent with one another, suggesting a sharp increase in reflectivity at 425GPa.” We have criticized this claim in an article for Advances in Physics, which was published after Ackland had submitted his letter to Inference.38 Loubeyre et al. made no measurements of the conductivity or reflectance of their samples.39
Ackland deviates somewhat from the direction of our review in Inference and goes on to discuss quantum solids. He focuses on the fact that the isotope deuterium behaves differently than hydrogen, which is a fact. A different and more fundamental point of view is the notion of zero-point energy (ZPE). Consider a deuterium molecule. In a classical model in a molecular fixed reference frame on the molecule, the deuterons are bound and fixed in space due to the Coulomb interaction between the deuterons and electrons. In quantum mechanics, we must add the kinetic energy of the deuterons, Pi2/2m, where Pi is the momentum of the ith deuteron and m its mass. Deuterium has a very small mass and, as a consequence, large ZPE, so at a temperature of absolute zero the deuterons are moving in what is called zero-point motion. If the mass is reduced by a factor of two, there will be hydrogen and a larger ZPE. Hydrogen is expected to become metallic at a lower pressure than deuterium due to this ZPE. If mass could be further reduced until the ZPE is equal to the binding energy, the molecule would dissociate into two atoms.
Ackland also discusses superconductivity and hydrides, that is, solids that are rich in hydrogen with stoichiometrically embedded atoms, such as sulfur and lithium. These compounds have high superconducting transition temperatures. This subject, as well, deviates from the point of our essay. Nonetheless, it is expected that pure metallic hydrogen would have a high superconducting transition temperature.40
In our review for Inference, we examined the progress and advances in the study of metallic hydrogen, including our achievement of creating metallic hydrogen at low temperature and high pressure, with spectral measurements of the reflectance as proof of the accomplishment. Ackland criticizes our result without providing an adequately thought-through argument, and he uncritically accepts the problematic opinions of other reviewers. He seems to focus on experiments in which molecular hydrogen may be a metal, rather than the Wigner–Huntington transition to atomic metallic hydrogen. At this time, there exists no convincing evidence such as metallic reflectance for molecular metallic hydrogen.
