Physicists see hints of Majorana fermions

Magnetic diffraction pattern for a Josephson junction with a topological insulator weak link. The horizontal axis is the applied magnetic field, the vertical axis is the current through the junction. The colours represent the differential resistance with white being zero. (Courtesy: Phys. Rev. Lett.)

Evidence for the existence of “Majorana fermions” – theoretically proposed particles that are also their own anti-particles – could be seen in the behaviour of a novel Josephson junction. That is the view of physicists at Stanford University in the US, who have examined the properties of a Josephson junction that incorporates material called a “topological insulator” sandwiched between two superconducting contacts. The researchers found significant deviations from what is seen in conventional Josephson junctions – differences that they believe could be explained in terms of Majorana-like quasiparticles.
First predicted by the Italian physicist Ettore Majorana in 1937 – shortly before he mysteriously disappeared aged just 31 – Majorana fermions are interesting not just because they are their own antiparticles but also because they should be resistant to environmental noise. Majorana fermions, in other words, could be used to store and transmit quantum information without being perturbed by the outside world, which is the bane of anyone trying to build a practical quantum computer.
Although definite proof of the existence of Majorana fermions has not yet been obtained, theorists have calculated that particle-like excitations, or quasiparticles, which look like Majorana fermions could exist at the interface where a topological insulator – a material that only conducts electricity on its surface – is placed next to an ordinary superconductor. These quasiparticles are called “zero-energy modes” because they lie along the Fermi energy of the material.
In the case of a Josephson junction containing a topological insulator as the “weak link” between two superconductors, there are actually two superconductor–topological insulator interfaces back-to-back, and the Majoranas are expected to couple to each other and depart from zero energy. However, if a tiny magnetic field – even as small as half a superconducting flux quantum – is applied to the junction, the two Majorana modes decouple and both reside at zero energy.

The weakest link

David Goldhaber-Gordon and colleagues at Stanford have now studied such junctions and have found some bizarre behaviour, which they have tried to explain in terms of Majorana fermions. When experimentalists plot a graph of the superconducting current flowing across a Josephson junction against the value of an applied magnetic field, they usually see a distinct “magnetic diffraction pattern” (MDP). Normally, the MDP has a strong central peak, but in topological-insulator Josephson junctions, Goldhaber-Gordon and colleagues saw a much more complicated MDP with several unexpected peaks. Indeed, the first minimum occurs at about one-fifth of the magnetic field strength that is expected in a conventional Josephson junction.
According to Goldhaber-Gordon, this more complicated structure could be related to the zero-energy Majorana modes that are expected to occur at specific values of magnetic flux. However, to explain the observed diffraction pattern, Goldhaber-Gordon points out that three – rather than one – zero-energy modes are required. One of these modes could be associated with a Majorana fermion, whereas the other two could be associated with other conventional fermions – something that Goldhaber-Gordon says has been suggested by some theorists.

Smaller critical currents

Another atypical feature seen by the team is the value of the device’s critical current (above which it no longer superconducts) multiplied by its resistance in the normal, non-superconducting state. This product is usually proportional to the superconducting energy gap, but the team measured a value that is much smaller than expected. The value was also found to be inversely proportional to the width of the Josephson-junction device – that is, the distance across the device perpendicular to the flow of the supercurrent.
Building on a theoretical description published in 2008 by Charles Kane and Liang Fu at the University of Pennsylvania in the US, Goldhaber-Gordon and colleagues assume that the Majorana fermions are confined to a 1D wire that runs along the width of the Josephson junction. The result is a series of quantized energy levels that are inversely proportional to the width of the device. The team speculates that the gap between these energy levels provides a new and smaller energy scale above which superconductivity ceases to occur – explaining the smaller measured values.
Although the team analysed its results in the context of Majorana fermions, Goldhaber-Gordon stresses that his team are still only at the early stages of exploring the behaviour of junctions between superconductors and topological insulators. “Many aspects of the materials and junctions are not yet well understood,” he says. “We welcome ideas for the explanation of these data, whether they are Majorana-related, or not.”

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Physicists Apply Einstein’s General Theory of Relativity to Superconducting Circuits

In recent years, UC Santa Barbara scientists showed that they could reproduce a basic superconductor using Einstein’s general theory of relativity. Now, using the same theory, they have demonstrated that the Josephson junction could be reproduced. The results are explained in a recent issue of the journal Physical Review Letters.

The gravitational description of the superconducting condensate shows a suppression in the gap.

The Josephson junction, a device that was first discovered by Brian David Josephson in the early 1960’s, is a main ingredient in applications of superconductivity.
Gary Horowitz, professor of physics at UCSB, said that Einstein’s general theory of relativity — which was developed as a theory of gravity and is extremely successful in explaining a wide variety of gravitational phenomena — is now being used to explain several aspects of non-gravitational physics.
“The basic phenomenon with Josephson junctions is that you can take two superconductors, separate them by a little gap, and still find current going across it, in a specific way,” said Horowitz. “And that has found many applications. So the Josephson junction is something we’ve reproduced using general relativity.”
Horowitz said that he and his co-authors used tools from string theory to develop the gravity model of a superconductor. He explained that it was surprising to be able to link Einstein’s general theory of relativity to a totally different area of physics. He said he hoped that the new tools would one day be able to shed light on new types of superconductors.
“Most materials, if you cool them down sufficiently, will actually conduct electricity without any resistance,” said Horowitz. “These are superconductors. There is a standard theory of superconductivity, discovered about 50 years ago, that has worked well for most of the so-called conventional superconductors.”
A new class of materials was discovered 25 years ago. These are superconductors that have zero resistance at somewhat higher temperatures. Physicists are still working on understanding the mechanism.
This new class of materials involves copper-oxygen planes. Another new class of superconductors, based on iron instead of copper, was discovered a couple of years ago. These materials, called iron nictides, also have the property of superconducting at a higher temperature.
“There is a lot of activity and interest in understanding these materials,” said Horowitz. “Ultimately, the goal is to have a room-temperature superconductor, which, you can imagine, would have lots of interesting applications.”
Horowitz and his research team found what could be called a gravitational model, or a gravitational dual — a dual description of a superconductor using gravity, black holes, and all of the traditional ingredients of general relativity. “This came as quite a surprise because this is a totally different area of physics, which is now being connected to this condensed matter area,” said Horowitz.
The co-authors of the paper are postdoctoral fellow Jorge E. Santos and graduate student Benson Way.