How black holes can be used as models for superconductors

Physicists at the University of Illinois at Urbana-Champaign have shown how charged black holes can be used to model the behaviour of interacting electrons in unconventional superconductors.

“The context of this problem is high-temperature superconductivity. 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,” said Philip W. Phillips.

Current semiconductors start off their lives as insulators. In this stage, 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 arises from the strong repulsions between the electrons.

Phillips and colleagues wondered, “Is it possible to devise a theory of gravity that mimics a Mott insulator?” As it turned out, there 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 shows that the boundary of the spacetime consisting of a charged black hole and weakly interacting electrons exhibits a barrier for electrons moving in that region, just as in the Mott state.

“The next big question that we must address,” said Phillips, “is how does superconductivity emerge from the gravity theory of a Mott insulator?”

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The results of research were published online in Physical Review Letters on March 1 and in Physical Review D on February 25. (ANI)

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