In a deceptively drab black crystal, physicists have stumbled upon a baffling behavior, one that appears to blur the line between the properties of metals, in which electrons flow freely, and those of insulators, in which electrons are effectively stuck in place. The crystal exhibits hallmarks of both simultaneously.

“This is a big shock,” said Suchitra Sebastian, a condensed matter physicist at the University of Cambridge whose findings appeared today in an advance online edition of the journal Science. Insulators and metals are essentially opposites, she said. “But somehow, it’s a material that’s both. It’s contrary to everything that we know.”

“It is just a magnificent paradox,” said Jan Zaanen, a condensed matter theorist at Leiden University in the Netherlands. “On the basis of established wisdoms this cannot possibly happen, and henceforth completely new physics should be at work.”

It is too soon to tell what, if anything, this “new physics” will be good for, but physicists like Victor Galitski, of the University of Maryland, College Park, say it is well worth the effort to find out. “Oftentimes,” he said, “big discoveries are really puzzling things, like superconductivity.” That phenomenon, discovered in 1911, took nearly half a century to understand, and it now generates the world’s most powerful magnets, such as those that accelerate particles through the 17-mile tunnel of the Large Hadron Collider in Switzerland.

Theorists have already begun to venture guesses as to what might be going on inside SmB6. One promising approach models the material as a higher-dimensional black hole. But no theory yet captures the whole story. “I do not think that there is any remotely credible hypothesis proposed at this moment in time,” Zaanen said.

SmB6 has resisted classification since Soviet scientists first studied its properties in the early 1960s, followed by better-known experiments at Bell Labs.

Counting up the electrons in the orbital shells that surround its samarium and boron nuclei indicates that roughly half an electron should be left over, on average, per samarium nucleus (a fraction, because the nuclei have “mixed valence,” or alternating numbers of orbiting electrons). These “conduction electrons” should flow through the material like water flowing through a pipe, and thus, SmB6 should be a metal. “That’s the idea people had back when I started working on this problem as a young guy, around 1975,” said Jim Allen, an experimental physicist at the University of Michigan in Ann Arbor who has studied SmB6 on and off since then.

But while samarium hexaboride does conduct electricity at room temperature, things get strange as it cools. The crystal is what physicists call a “strongly correlated” material; its electrons acutely feel one another’s effects, causing them to lock together into an emergent, collective behavior. Whereas strong correlations in certain superconductors cause the electrical resistance to drop to zero at low temperatures, in the case of SmB6, the electrons seem to gum up when cooled, and the material behaves as an insulator.

The effect stems from the 5.5 electrons, on average, that occupy an uncomfortably tight shell encasing each samarium nucleus. These close-knit electrons mutually repel one another, and “that essentially tells the electrons, ‘Don’t move around,’” Allen explained. The last half electron trapped in each of these shells has a complex relationship with its other, freer, conducting half. Below minus 223 degrees Celsius, the conduction electrons in SmB6 are thought to “hybridize” with these trapped electrons, forming a new, hybrid orbit around the samarium nuclei. Experts initially believed the crystal turns into an insulator because none of the electrons in this hybrid orbit can move.

“The resistivity shows it’s an insulator; photoemission shows it’s a good insulator; optical absorption shows it’s a good insulator; neutron scattering shows it’s an insulator,” said Lu Li, a condensed matter physicist at the University of Michigan whose experimental group also studies SmB6.

But this is no garden-variety insulator. Not only does its insulating behavior arise from strong correlations between its electrons, but in the past five years, mounting evidence has suggested that it is a “topological insulator” at low temperatures, a material that resists the flow of electricity through its three-dimensional bulk, while conducting electricity along its two-dimensional surfaces. Topological insulators have become one of the hottest topics in condensed matter physics since their 2007 discovery because of their potential use inquantum computers and other novel devices. And yet, SmB6does not neatly fit that category either.

Early last year, hoping to add to the evidence that SmB6 is a topological insulator, Sebastian and her student Beng Tan visited the National High Magnetic Field Laboratory, or MagLab, at Los Alamos National Laboratory in New Mexico and attempted to measure wavelike undulations called “quantum oscillations” in the electrical resistance of their crystal samples. The rate of quantum oscillations and how they vary as the sample is rotated can be used to map out the “Fermi surface” of the crystal, a signature property “which is sort of the geometry of how the electrons flow through the material,” Sebastian explained.

Sebastian and Tan didn’t see any quantum oscillations in New Mexico, however. Scrambling to salvage Tan’s doctoral project, they measured a less interesting property instead, and, to check these results, booked time at another MagLab location, in Tallahassee, Fla.