Many of the great successes of particle physics involve symmetries of nature and the occasional violation of those symmetries. Discoveries such as the Higgs boson are strong vindications of this view of the world and of the Standard Model that describes these particles.

An extension to the Standard Model, called supersymmetry, takes this idea further by incorporating symmetries of space-time, as the name suggests. One side effect of supersymmetry in particle physics is the prediction of a partner to each known particle, which (among other things) could help solve the mystery of dark matter.

Despite intensive searches at the Large Hadron Collider, none of these supersymmetric partners have been detected in nature yet. However, Tarun Grover, D. N. Sheng, and Ashvin Vishwanath proposed in a new paper that an analog of supersymmetry could exist in certain exotic superconducting systems. By manipulating the characteristics of materials called "topological superconductors," researchers should be able to change particle-like excitations into their supersymmetric partners. The similarity in the physical description of these different systems could provide some important insights into the possible nature of supersymmetry and its violation in nature.

The fundamental constituents of matter—electrons, quarks, and their relatives—are known as fermions; the particles associated with fundamental forces are bosons. (The names are in honor of Italian physicist Enrico Fermi and Indian physicist Satyendra Nath Bose.) The Standard Model of particle physics explains the relationship between these particles and the symmetries that govern their behavior. In particular, the Higgs boson is the result of an imperfect symmetry inherent in the weak force.

Space-time itself also possesses certain symmetries, which are described in the theory of relativity. Additionally, Noether's theorem (discovered by German mathematician Emmy Noether) states that a symmetry implies a conservation law. Moving a physical system—a decaying atomic nucleus, for example—an arbitrary distance shouldn't affect the decay behavior. That invariance is known as translational symmetry, and Noether's theorem associates it with the conservation of momentum.

Combining the rules of particle physics and this translational symmetry (along with some other aspects of relativity) yields supersymmetry, often abbreviated as SUSY. The side effect of this symmetry: every boson should have a fermion partner and vice versa.

Except they don't. There are more fermions than bosons in the Standard Model, and we don't see these partners in ordinary experiments. So, if it exists, SUSY must be a broken symmetry of nature. The predicted consequence of this brokenness is that the SUSY particles (which have Jabberwockian names like "squark" and "bino") should be much more massive than their Standard Model counterparts. In particular, the lowest-mass SUSY particles are heavy enough to be dark matter particles.

To date, particle physics experiments have yet to turn up any sign of SUSY. However, a number of theories over the years have postulated equivalent behavior could exist in certain very cold materials. In such systems, interactions between electrons and atoms produce quasiparticles—particle-like excitations that can have masses, electric charges, and magnetic properties very different from the electrons that created them. Quasiparticles can act like free particles that move close to the speed of light, and their interactions can mimic the behavior of the Higgs field and other complex phenomena in particle physics.

The new paper discussed the idea of emergent SUSY-like behavior in topological superconductors. In these systems (described in more detail in the sidebar story), the interior of the material conducts electricity without resistance, but the outside is an ordinary conductor. The authors argued that experimentally observed magnetic behavior on the conducting surface could be interpreted super symmetrically. It also exhibits a breaking of SUSY due to the fundamental difference in interior and surface behavior of the system.

In this view, the magnetic excitations (acting like bosons) on the surface are SUSY partners with the topological superconductor quasiparticles, which are fermions. The behavior of this system (due to the nature of the materials) is two- or three-dimensional, whereas the SUSY of particle physics is four-dimensional. Nevertheless, the paper makes a strong argument that a direct analog to SUSY could already exist in exotic materials—an important result.

The question we must ask, of course, is whether emergent supersymmetric behavior—however intriguing—tells us anything about the nature of fundamental particles. (Physicists have a similar conundrum with the quantum simulation of a magnetic monopole.) To phrase it another way: we don't know if SUSY partners exist as fundamental particles in this Universe, regardless of whether topological superconductors behave the way physicists predict they should. These materials are interesting in their own right, however, and their study reveals a lot about the nature of collective quantum systems.

Science, 2014. DOI: 10.1126/science.1248253 (About DOIs).