Quantum and relativistic effects explain why mercury is superconducting

Mercury is an amazing element in more ways than one. At room temperature, this silvery-looking metal is liquid. For this reason, it was used in thermometers long before it was banned due to its toxicity. But it was another property that intrigued Cesare Tresca, of the University of L’Aquila, Italy, and colleagues. In 1911, Heike Kamerlingh Onnes found that in mercury cooled to a few degrees above absolute zero (-273°C), electric current flows without resistance. Hence it has shed light on the phenomenon of superconductivity. But so far, no model has been able to satisfactorily describe the onset of this state in Hg. The team around Cesare Tresca solves this exception.

At normal atmospheric pressure, mercury becomes solid at 234 K (-38 °C) and its electrical resistance disappears below 4.15 K, which we are talking about its critical temperature. Many materials are superconductors with critical temperatures in this order. In 1957, John Bardeen, Leon Cooper, and John Shriver (BCS) demonstrated on a microscopic scale how these materials become superconductors. In general, electrons, current carriers, circulate in a conductive metal but tend to interact strongly with the material’s crystal lattice, hindering its movement. This effect is nothing but the electrical resistance of the material. But in a superconducting material, by bonding in pairs, called “Cooper pairs,” the electrons are no longer subject to interactions with the medium. However, the formation of these pairs is paradoxical, because the electrons, being negatively charged, should repel each other. BCS theory shows that the vibrations of the crystal lattice (which we talk about as “phonons”) help to stabilize these pairs despite the Coulomb repulsion. This effect is fragile and only works at very low temperatures: at a higher temperature, thermal stirring is sufficient to destroy the cohesion of the pairs.

The BCS theory fully explains the appearance of superconductivity at temperatures close to absolute zero. However, since the 1980s, new superconducting materials have been discovered with critical temperatures of several tens of kelvins, and we are talking about “high-temperature” superconductors. This phenomenon still needs to be explained.

Mercury belongs to the class of conventional superconductors. However, neither the BCS theory nor the more advanced methods developed later make it possible to satisfactorily calculate their properties, in particular their critical temperature.

Cesar Tresca and colleagues set out to study the properties of mercury to understand this exception. Thus they found that all the physical properties involved in a conventional superconductor are abnormal in this metal: its electronic structure, scattering of phonons, interactions of electrons with phonons, etc.

Starting with the crystal structure of solid mercury, the researchers incorporated influences that are generally ignored in the calculations to more precisely recover the properties of this metal. In an atom, electrons can only occupy certain energy levels, which are divided into layers denoted s, p, d, etc. The researchers took into account, for example, the effect of relative coupling between the s and d layers. Relativistic effects also affect the dynamics of the phonons. All these effects profoundly modify d shells, which in turn limit the Coulomb repulsion and thus promote the formation of Cooper pairs.

With their new model, the researchers calculated the critical temperature for mercury and got a value of 4.05 K, a difference of only 2.5% with the experimental value. This value is obtained from the sole laws of relativistic quantum mechanics without adding any experimental parameter. The case of mercury appears to be universally resolved and opens up a line of thought for high-temperature superconductors: it may be necessary to consider some hitherto neglected effects to describe them better.