Feature

# Reversing a Quantum Force

Phys. Rev. Focus 27, 1
Two objects made of the exotic materials known as topological insulators could repel one another through the quantum-mechanical forces that cause most other solids to attract, theorists predict.

Usually there is a tiny attraction between two objects that are nearly touching, because of the way they tweak the quantum-mechanical energy of empty space. But in the 14 January Physical Review Letters theorists propose that if the objects are made of the newly-discovered materials known as topological insulators, they can be arranged to either attract or repel one another. Although not the first example of such a repulsion, the result could give insight into both the new materials and the exotic force.

Even in complete darkness, quantum mechanics dictates that electromagnetic fields hum with tiny oscillations that cannot be eliminated. But they can be modified: just as fixing the ends of a guitar string restricts its possible vibrations, electromagnetic oscillations are constrained in the gap between two solid surfaces. For normal materials, the energy stored in the fields decreases as the solids get closer, which gives rise to an attraction known as the Casimir force.

Alberto Cortijo, now at the Autonomous University of Madrid, and graduate student Adolfo Grushin wondered how this force would differ when acting between topological insulators, exotic states of solids whose existence has recently been confirmed in real crystals. Electric current in such a material flows only on its surface and is not disrupted by crystal defects, theorists predict. They also expect electromagnetic fields to behave in unusual ways in the middle of the solid. For example, static electric and magnetic fields don’t normally influence each other directly, but inside a topological insulator, they can interact. Although a similar interaction occurs in some other materials, it varies with details such as the light frequency. By contrast, in a topological insulator, the interaction is simply proportional to a so-called magnetoelectric coupling constant that is an odd multiple of pi.

The Casimir effect depends on the way electromagnetic waves reflect off of the two surfaces. But the conducting surface of a topological insulator would reflect in a way similar to an ordinary, shiny metal and prevent the waves from penetrating to the exotic environment inside. So Cortijo and Grushin propose using a trick other theorists have suggested for getting waves past the surface: coat the topological insulator with a thin magnetic film that prevents it from conducting current.

Some electromagnetic waves will then reflect off of the crystal in unusual ways because of the magnetoelectric coupling inside, according to Grushin and Cortijo’s calculations. For example, the polarizations of the waves will be scrambled by the reflection in a way different from conventional materials. This polarization scrambling changes the energy stored in electromagnetic fields between the two topological insulators and leads to a Casimir repulsion under some conditions.

The effect depends on the value of the magnetoelectric coupling parameter, which is determined by details of the material. But it can also be influenced by the direction of magnetization in the coating. Grushin and Cortijo found that when the coupling parameter has the same sign in both topological insulators, the ordinary Casimir attraction occurs. But when the signs are opposite in the two materials, the surfaces will repel if they get too close, perhaps within a fraction of a micron. So the short-range force could be changed from attractive to repulsive by changing the coating. Previous experiments have demonstrated a repulsive Casimir force, but only in the presence of a third material, such as a surrounding liquid [1].

The effect of magnetoelectric coupling on the Casimir force was not known before, says Joel Moore of the University of California, Berkeley, and Lawrence Berkeley National Lab, even though other consequences of the coupling were explored theoretically 20 years ago. Still, he cautions that to see this and other macroscopic effects, experimentalists will need to produce more precisely engineered materials. Just the right number of electrons are needed at the surface to allow a magnetic film to freeze them out. “So far no one has been able to go to the next step to be able to provide a strong enough perturbation to make the surface really insulating,” he says.

–Don Monroe

Don Monroe is a freelance science writer in Murray Hill, New Jersey.

## References

1. J. N. Munday, F. Capasso, and V. A. Parsegian, “Measured Long-Range Repulsive Casimir–Lifshitz Forces,” Nature 457, 170 (2009)

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