# Superconductors via Superstrings

Nature has an article about a nifty and relatively new application of ideas born out of string theory: to understand what happens in high-temperature superconductors! The story goes something like this.

Take a sample of some material which can conduct electricity, and apply two kinds of outside influence upon it. First, stick it in a magnetic field pointing in some direction, and second, apply a temperature gradient in a direction perpendicular to the magnetic field. In some substances, an electric field will appear, perpendicular to both the magnetic field and the temperature gradient. This is called the Nernst effect. It doesn’t happen very much with ordinary metals, but in semiconductors — like silicon or germanium — it can be quite noticeable. It also appears in some superconductors, like Y-Ba-Cu-O and CeCoIn5 to name but two.

Sean A. Hartnoll et al. have cooked up a theory to explain the Nernst effect and other behaviors seen in the cuprate superconductors, ceramic compounds containing copper. Looking at the situation near the phase transition, where a substance is “on the verge” of changing from insulator to superconductor, they developed a theory involving the magnetic field, call it $B$, and fluctuations in the material’s density, $\rho$. Then they looked at this theory in the conceptual mirror known as the AdS/CFT correspondence. This connection between seemingly disparate ideas takes you from a “conformal field theory,” the sort of math involved with the superconductor problem (among other things), to a theory of gravity in a type of universe called anti-de Sitter space. In this mirror-world description, the perturbations in $B$ and $\rho$ become magnetic and electric charges of a black hole sitting in the AdS universe!

This chicanery becomes useful because easy problems in one description often correspond to hard problems in the other. Thus, you can study the black hole and learn about its counterpart, even when the counterpart is too complicated to approach directly.

Hartnoll and company were able to extract details on how their superconductor model behaves by looking at its black-hole dual. In their words,

This is the power of the AdS/CFT correspondence: all transport phenomena of the strongly correlated CFT at large N are reduced to solving the equations for classical perturbations of the dual black hole in Einstein-Maxwell theory.

SEE:

• Hartnoll, S.A., Kovtun, P.K., MÃ¼ller, M., Sachdev, S. (2007). Theory of the Nernst effect near quantum phase transitions in condensed matter and in dyonic black holes. Physical Review B, 76(14) DOI: 10.1103/PhysRevB.76.144502; arXiv:0706.3215.

## 5 thoughts on “Superconductors via Superstrings”

1. OK, learning curve still high, but thanks to your previous post on AdS/CFT understood a little bit better. And I actually kind of was intrigued. I guess that’s progress for this guy, though you fellas seem to give the lie to the claim that there is math that stops everyone. Good stuff!

2. Yeah, I had to toss this post off quickly in between other things. . . Someday, I’ll find a nice solid block of time in which I can explain AdS/CFT from the beginning.

3. Well, this certainly sounds cool. Was hoping they’d be able to find a possible application for strings. Trying to find testable predictions has been pretty difficult, so it looks like they may be able to move beyond speculation that fits the math and into scientific testing.

I think strings are a cool, elegant idea from what I’ve seen, but I know to keep in mind that there’s always an idea that’s simple, elegant, beautiful, and wrong.

4. Bronze Dog:

This is just the most recent application of AdS/CFT to have hit the journals. They’ve been applying it to quark-gluon plasmas, the high-energy state of matter you get when you mush two heavy nuclei together at stupendous speeds, and so far, nice qualitative results have come out, which everybody is working on improving and sharpening.

String theory ain’t just people sitting around wanking about the Anthropic Principle!

5. Well, I’m in favor of any theory that’s not (blushing) hand, um, waving.