Black holes: a model for superconductors?

Celia Elliott

Urbana, Ill.—Black holes are some of the heaviest objects in the universe. Electrons are some of the lightest. Now Professors Robert G. Leigh and Philip Phillips, along with postdoctoral fellow Mohammad Edalati and graduate student Ka Wai Lo, of the University of Illinois have shown how charged black holes can be used to model the behavior of interacting electrons in unconventional superconductors. Their results were published online in Physical Review Letters on March 1 and in Physical Review D on February 25.

“The context of this problem is high-temperature superconductivity,” said Phillips. “One of the great unsolved problems in physics is the origin of superconductivity (a conducting state with zero resistance) in the copper oxide ceramics discovered in 1986.”

Mohammad Edalati, Rob Leigh, and Philip Phillips <br />
Department of Physics, University of Illinois<br />
Photo by Rick Kubetz
Mohammad Edalati, Rob Leigh, and Philip Phillips
Department of Physics, University of Illinois
Photo by Rick Kubetz

Unlike the old superconductors, which were all metals, the new superconductors start off their lives as insulators. In the insulating state of the copper-oxide materials, there are plenty of places for the electrons to hop but nonetheless—no current flows. Such a state of matter, known as a Mott insulator after the pioneering work of Sir Neville Mott, arises from the strong repulsions between the electrons. Although this much is agreed upon, much of the physics of Mott insulators remains unsolved, because there is no exact solution to the Mott problem that is directly applicable to the copper-oxide materials.

Enter string theory—an evolving theoretical effort that seeks to describe the known fundamental forces of nature, including gravity, and their interactions with matter in a single, mathematically complete system.

In string theory, some strongly interacting quantum mechanical systems can be studied by replacing them with classical gravity in a space-time in one higher dimension, a relationship that was first conjectured by string theorist Juan Maldacena some 14 years ago. The conjecture was made possible by thinking about D-branes, important objects in string theory, in two different but equivalent ways. Physical features of the quantum systems, such as temperature, charge density, etc., become properties of black holes in the classical gravity theory.

Since most condensed matter phenomena involve electron physics, Leigh, along with graduate student Juan Jottar, set out to investigate the sorts of interactions that electrons might have in classical gravity theories that arise in string theory. Since the Mott problem is an example of strongly interacting particles, Edalati, Leigh and Philips then asked the question: "Is it possible to devise a theory of gravity that mimics a Mott insulator?” Indeed it is.

The researchers built on Maldacena’s mapping and devised a model for electrons moving in a curved spacetime in the presence of a charged black hole that captures two of the striking features of the normal state of high-temperature superconductors: 1) the presence of a barrier for electron motion in the Mott state, and 2) the strange metal regime in which the electrical resistivity scales as a linear function of temperature, as opposed to the quadratic dependence exhibited by standard metals.

The treatment advanced in the paper published in Physical Review Letters represents the first time a resolution of the Mott problem has been observed in a two-dimensional system, the relevant dimension for the high-temperature superconductors. The next big question that must be addressed is how superconductivity might emerge from the gravity theory of a Mott insulator.

Recent News

  • In the Media

Albert Einstein was right again. More than 100 years ago, his calculations suggested that when too much energy or matter is concentrated in one place, it will collapse in on itself and turn into a dark vortex of nothingness. Physicists found evidence to support Einstein’s black hole concept, but they’d never observed one directly. In 2017, 200-plus scientists affiliated with more than 60 institutions set out to change that, using eight global radio observatories to chart the sky for 10 days. In April they released their findings, which included an image of a dark circle surrounded by a fiery doughnut (the galaxy Messier 87), 55 million light years away and 6.5 billion times more massive than our sun. “We have seen what we thought was unseeable,” said Shep Doeleman, leader of what came to be known as the Event Horizon Telescope team. The team’s name refers to the edge of a black hole, the point beyond which light and matter cannot escape. In some ways, the first picture of a black hole is also the first picture of nothing.

Institute for Condensed Matter Theory in the Department of Physics at the University of Illinois at Urbana-Champaign has recently received a five-year grant of over $1 million from the Gordon and Betty Moore Foundation. The grant is part of the Gordon and Betty Moore Foundation’s Emergent Phenomena in Quantum Systems (EPiQS) Initiative, which strives to catalyze major discoveries in the field of quantum materials—solids and engineered structures characterized by novel quantum phases of matter and exotic cooperative behaviors of electrons. This is the second 5-year EPiQS grant awarded to the ICMT by the Moore Foundation. The two awards establish an EPiQS Theory Center at the Institute for Condensed Matter Theory.

  • Outreach
  • Accessibility

University of Illinois at Urbana-Champaign physics graduate student Colin Lualdi quickly realized he was venturing into uncharted territory when he arrived at Illinois Physics at the start of Fall 2017. Deaf since birth and a native speaker of American Sign Language (ASL), Lualdi was now among a very small group worldwide of Deaf individuals working in physics. The exhilaration of performing cutting-edge research was accompanied by a sobering discovery: the lack of a common language model for effective scientific discourse in ASL was going to be a far greater challenge than he’d anticipated. Lualdi has embraced his own accessibility challenges as an opportunity to address a pressing need in the broader Deaf community. He has teamed up with colleagues at other research institutions to develop a robust and shared framework for scientific discourse in ASL. Specifically, Colin has been working with ASL Clear and ASLCORE, two national scientific sign language initiatives that are making good progress.