Mottness from a Black Hole. Credit: Univ. of Illinois at Urbana-Champaign. |
Black holes are some of the heaviest
objects in the universe. Electrons are some of the lightest. Now physicists at Illinois have shown how
charged black holes can be used to model the behavior of interacting electrons
in unconventional superconductors.
“The context of this problem is
high-temperature superconductivity,” said Philip Phillips, a professor of physics.
“One of the great unsolved problems in physics is the origin of superconductivity
in the copper oxide ceramics discovered in 1986.” The results of research by
Phillips and his colleagues Robert G. Leigh, Mohammad Edalati, and Ka Wai Lo
were published online in Physical Review Letters and in Physical Review D.
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.
Fourteen years ago, a string theorist, Juan
Maldacena, conjectured that some strongly interacting quantum mechanical
systems could be modeled by classical gravity in a spacetime having constant
negative curvature. The charges in the quantum system are replaced by a charged
black hole in the curved spacetime, thereby wedding the geometry of spacetime
with quantum mechanics.
Since the Mott problem is an example of
strongly interacting particles, Phillips and colleagues asked the question: “Is
it possible to devise a theory of gravity that mimics a Mott insulator?” Indeed
it is, as they have shown.
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
shows surprisingly 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. This work represents the
first time the Mott problem has been solved (essentially exactly) in a
two-dimensional system, the relevant dimension for the high-temperature
superconductors.
“The next big question that we must address,”
said Phillips, “is how does superconductivity emerge from the gravity theory of
a Mott insulator?”
This research was supported by the National
Science Foundation and the Center for Emergent Superconductivity, a DOE Energy
Frontier Research
Center.
