By Eugenie Samuel Reich

String theory, which some physicists hope may be able to unify gravity and quantum mechanics, may have found a real-world application. A type of black hole predicted by string theory may help to explain the properties of a mysterious class of materials called 'strange metals'.

The electrical resistance of strange metals increases linearly with temperature rather than with the square of the temperature as in normal metals. They also have other excitations of energy that can be thought of as especially short-lived particles.

Strange metals include high-temperature superconductors, which have no electrical resistance at all below a critical temperature that is generally defined as above the boiling point of liquid nitrogen (196 °C). Their properties have baffled condensed matter physicists for over 20 years because strange metals cannot be explained by the Fermi liquid model, which captures the properties of normal metals.

In 2003, condensed matter physicist Subir Sachdev of Harvard University, in Cambridge, Massachusetts, and his colleagues, put forward a new model called fractionalized Fermi liquid (FFL) that seemed to account for some of the properties of strange metals, including the variation of their resistance with temperature1. Unlike in the standard Fermi liquid model, the quantum mechanical spins of some electrons in the material are linked together in an FFL.

Now, in a paper published in Physical Review Letters2 on 4 October, Sachdev shows that the FFL model's characteristics match those of a type of black hole in string theory. "We're still a long way from saying string theory explains strange matter but we have hope," Sachdev says. "It's very exciting because it's a whole new perspective." He adds that he's been learning string theory at a breakneck speed.

Smear to lattice

Sachdev's result built on work by theoretical physicist John McGreevy of MIT and his colleagues, who in 2009 began applying a string theory conjecture known as the AdS/CFT correspondence to strange metals. The AdS/CFT correspondence sets up a mathematical equivalence between quantum systems and gravitational objects. McGreevy admits the quantum systems he and his colleagues studied were very abstract because they had properties that were smeared out continuously in space instead of varying in a stepwise, quantum fashion.Sachdev's has come up with a more realistic model, McGreevy says, by applying a gravitational object, a kind of black hole, to a quantum system with properties that vary stepwise along a lattice, just as in the lattice structure of strange metals. "It's still not a model of a real material but it's progress in that direction," says McGreevy.

It is not the first time that string theory has been applied to a problem in condensed matter physics. In 2004, Pavel Kovtun, now at the University of Victoria in British Columbia, Canada, and his colleagues used string theory to describe a soup of fundamental particles called a quark-gluon plasma created in collisions at the RHIC accelerator at Brookhaven National Laboratory in Upton, New York. But that has been considered a fairly isolated example, and other attempts to apply the AdS/CFT correspondence to condensed matter systems including superconductors haven't really managed to connect with a realistic model, says Joe Polchinski, a string theorist at the University of California, Santa Barbara.

Physics frontier

The hope is that tricks from string theory can now be used to make progress on improving the FFL model. One of its problematic aspects is the prediction of a state of matter that still has some level of order (non-zero entropy) at absolute zero (0 Kelvin). This violates the third law of thermodynamics, which says that, for FFLs, entropy should tend to zero as the system is cooled to absolute zero. Sachdev says he always considered this a shortcoming of his theory, but other physicists took the view that it might instead be saying something profound about real materials. "We never knew whether it was a bug or a feature," says Polchinski.

In his latest work, Sachdev shows that the string theory version of the FFL model also violates the third law of thermodynamics at absolute zero. The emergence of the same problem in a totally different mathematical framework suggests it is pointing to something in the real world, Polchinski says. Sachdev says more work will be needed to establish that for certain.

McGreevy suggests that the theory is signalling its own instability, so that a real material will change into another phase at a temperature higher than 0 K. In a commentary piece on Sachdev's article3, McGreevy says that high-temperature superconductors are known to change from strange metal behaviour to superconducting as they are cooled and so avoid getting into the zero-entropy state.

Even if string theory is successful in helping condensed matter physicists figure out strange metals, that won't necessarily mean that string theory is the correct description of fundamental particles and gravity. However, it will mean that string theory has been useful for something. "This is an important frontier," says McGreevy.