Mercury’s superconductivity explained at long last


A droplet of superconducting mercury levitating above a surface
Courtesy: Gianni Profeta and Cesare Tresca/University of L’Aquila

More than 100 years ago, the physicist Heike Kamerlingh Onnes discovered that solid mercury acts as a superconductor. Now, for the first time, physicists have a complete microscopic understanding of why this is so. Using a modern first-principles computational method, a team from the University of L’Aquila, Italy, found several anomalies in mercury’s electronic and lattice properties, including a hitherto undescribed electron screening effect that promotes superconductivity by reducing repulsion between pairs of superconducting electrons. The team also determined the theoretical temperature at which mercury’s superconducting phase transition occurs – information previously absent from condensed-matter textbooks.

Superconductivity is the ability of a material to conduct electricity without any resistance. It is observed in many materials when they are cooled below a critical temperature Tc that marks the transition to the superconducting state. In the Bardeen-Cooper-Schrieffer (BCS) theory of conventional superconductivity, this transition occurs when electrons overcome their mutual electrical repulsion to form so-called “Cooper pairs” that then travel unhindered through the material as a supercurrent.

Solid mercury became the first known superconductor in 1911, when Onnes cooled the element to liquid helium temperatures. While it was later classed as a conventional superconductor, its behaviour was never fully explained, nor was its critical temperature predicted – a situation that Gianna Profeta, who led the recent effort to repair this oversight, calls “ironic”.

“While its critical temperature is extremely low compared to high-Tc materials like the cuprates (copper oxides) and high-pressure hydrides, mercury has played a special role in the history of superconductivity, serving as an important benchmark for phenomenological theories in the early 1960s and 1970s,” Profeta says. “This is indeed ironic, that mercury, the element in which superconductivity was reported for the first time, had so far never been studied by modern first-principles methods for superconductors.”

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No empirical or even semi-empirical parameters required

In their work, Profeta and colleagues began with a counterfactual: if Onnes had not discovered superconductivity in mercury in 1911, could scientists predict its existence today using state-of-the-art computational techniques? To answer this question, they used an approach called SuperConducting Density Functional Theory (SCDFT), which is considered one of the most accurate ways of describing the superconducting properties of real-world materials.

In first-principles approaches like SCDFT, Profeta explains, the fundamental quantum mechanics equations describing the behaviour of nuclei and electrons in materials are solved numerically, without introducing any empirical or even semi-empirical parameters. The only information required by SCDFT is the arrangement in space of the atoms that form a given material, although some standard approximations are usually employed to keep computational times manageable.

Using this technique, the researchers found that a panoply of phenomena all come together to promote superconductivity in mercury. The behaviours they uncovered included unusual correlation effects on the material’s crystal structure; relativistic corrections to its electronic structure that alter the frequencies of phonons, which are vibrations of the crystal lattice; and an anomalous renormalization of the residual Coulomb repulsion between electrons due to low-lying (at about 10 eV) d-states.

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Such effects could be, and were, neglected in most (conventional) superconductors, Profeta says, but not in mercury. The screening effect, in particular, produces a 30% increase in the element’s effective critical temperature. “In this study, we realized that although mercury has been considered as being a rather simple system because of its uncomplicated structure and chemistry, it is in fact one of the most complex superconductors we had encountered,” Profeta tells Physics World.

Spin-orbit coupling effects are important

After taking all these factors into account, the researchers predicted a Tc for mercury that was within 2.5% of the actual experimentally measured value. They also found that if relativistic effects such as spin-orbit coupling (the interaction between the spin of an electron and its orbit around the atomic nucleus) were not included in the calculations, some phonon modes became unstable, indicating a tendency for the system to distort into a less symmetric structure. Such effects thus play a crucial role in determining mercury’s critical temperature. “As our everyday experience shows, mercury at room temperature is in a rather unusual liquid metal state, which is reflected in very low-energy (but not unstable) phonon modes,” explains Profeta. “Describing these modes accurately requires special care.”

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The researchers claim that their work, which is detailed in Physical Review B, is of historical importance. “We now know the microscopic mechanisms at play in the first ever discovered superconductor and have determined its superconducting phase transition – information that was lacking for the first ever superconductor to be discovered,” Profeta says.

This new understanding of the world’s oldest superconductor though a material-by-design approach was only possible thanks to high-throughput computations, he adds. Such computations are capable of screening millions of theoretical material combinations and picking out those that could be conventional superconductors at close to ambient conditions. Finding such room-temperature superconducting materials would vastly improve the efficiency of electrical generators and transmission lines, as well simplifying common applications of superconductivity such as superconducting magnets in particle accelerators and MRI machines.

“The peculiar Coulomb renormalization effects discovered in mercury could be exploited to engineer new materials, with an electronic density of states profile similar to mercury, providing an additional knob to enhance the critical temperature of materials,” Profeta says. “We are now exploring this possibility.”