léo ramosA group of Brazilian researchers has just planed and proposed some experiments that they believe would confirm, once and for all, the existence of one of the most elusive particles predicted by theoretical physicists: Majorana fermions, or simply majoranas, which have eluded all attempts at experimental detection. Results published with fanfare in the journal Science in 2012 seemed to have finally shown the existence of these particles, but the findings then began to be questioned. Now a Brazilian team of theoretical physicists studying condensed matter has created a new “recipe” to end this impasse and finally detect Majorana fermions, which may have interesting implications for the future of what is being called quantum computing. This area of research, which seeks to use the properties of subatomic particles to perform advanced computational operations, could use these particles to process information and perform calculations, since systems using Majorana fermions would be more stable than those using electrically charged particles such as electrons.
The strategies, published this year in the journal Physical Review B, were developed by José Carlos Egues, of the University of São Paulo (USP) Institute of Physics in São Carlos, and his team, consisting of Edson Vernek, a physicist at the Federal University of Uberlândia currently engaged in post-doctoral research with Egues, Poliana Penteado, of USP São Carlos and Antonio Carlos Seridonio, of the São Paulo State University (Unesp), Ilha Solteira. “We published a detailed proposal, with three different possible set-ups to create a system to verify the presence of this Majorana mode,” affirms Egues, who coordinated the work, which was highlighted in a special section of Physical Review B called Editors’ Suggestion, in which the most interesting articles of each edition are featured. Egues stresses, though, that extreme technical skill will be needed to implement the proposals.
In some respects, it seems appropriate that there is an aura of mystery about these particles, since they were named after the scientist who proposed their existence, Sicilian Ettore Majorana. He was born in 1906 and enjoyed a meteoric career before he vanished without a trace in 1938, during a sea voyage between Palermo and Naples. Messages left by the physicist insinuated that he had decided to commit suicide, but his body was never found, which prompted the emergence of far-fetched hypotheses, such as escape to Argentina or that he became a monk.
No matter what the truth really is, about a year before his fateful trip, Majorana found an innovative solution to the Dirac equation, which originally described the behavior of particles such as electrons with electric charge and spin (a property vaguely analogous to the rotation of a planet) equal to 1/2. In the case of electrons, this behavior is described by a complex wave function (containing both real and imaginary parts), which represents electrically charged particles. When working on variations of the Dirac equation—the mathematical formulation proposed by the British physicist Paul Dirac to describe electrons—Majorana discovered that another class of particles could be described by a real wave function (without the imaginary part). These particles without electrical charge are now called Majorana fermions.
“Some argue that one of the types of neutrinos could be the Majorana fermion, but particle physics studies have never reached a definitive conclusion,” says Egues. Thus, physicists began looking for the particle in condensed matter—for example, in electronic or other materials produced in the laboratory—rather than in the collisions of high-energy accelerators. Actually, they are investigating if a group of electrons in condensed matter could behave as if they were a single Majorana particle.
One of the principle means to determine this involves the creation of what are called quantum wires, on which Egues and his colleagues published another article in 2014 in Physical Review B, which was also featured in the Editors’ Suggestion section. From an intuitive point of view, perhaps the word “wire” is not the best term to describe the device, because it is normally a kind of channel, with a gauge of thousandths, or millionths, of a millimeter. It is created using a metal plate on which the researchers apply a delicate set of electric fields that “sweep” the electrons circulating in the material to two sides. “A channel is formed in the center region, and can be narrowed,” says Egues. At that point, electrons can be injected into the channel.
The next step is to attach the quantum wire to a superconductor, that is, to a material in which electrons can flow unimpeded, without the electrical resistance that characterizes normal metals. In the physically exotic context of superconductors, this movement is not of individual electrons, but rather of what are know an Cooper pairs—roughly speaking, electron pairs that “merge” to the extent that they appear to be a single entity. “The idea is that, if a superconductor is very near the material used for the quantum wire, the electrons in the non-superconducting material become ‘contaminated’ by the Cooper pairs,” explains Egues.
Leo Kouwenhoven and his colleagues at Delft Technological University, in the Netherlands, used a similar experimental design and reported observing Majorana fermions located at the system’s extremities, at the two ends of the quantum wire. “Detection” was via a peak in electrical conductivity at an unexpected energy level. “But other interpretations were proposed, and the matter was never resolved,” describes the physicist from USP.
In the new experimental design proposed by Egues and his colleagues, the question could be resolved by adding a quantum dot to the system, which could be described as the spherical equivalent of the quantum wire, produced by the same type of electron confinement. The Brazilian team’s calculations indicate that, using this set-up, the Majorana fermion would leave the wire, leaking into the quantum dot. In this way, a new energy level “that was not present in the quantum dot will appear,” and remain in the system and, thus, exclude possible explanations other than the presence of Majorana fermions, at least in principle. “It is important to stress that the Majorana fermions that appear in condensed matter experiments are not elementary particles,” mentions Egues. “In these tests, they appear as confined particles that behave according to equations similar to those developed by Majorana and produce measurable effects.”
“I don’t think this experiment could be carried out in Brazil, at least not now. It is not a question of money, but rather of know-how and quantum engineering,” states Egues. According to the physicist, one must have extensive expertise in each of the system’s components. “Even Kouwenhoven’s team, which has been working in this area since the 1980s, does not fully understand how it works,” he adds.
According to the physicist, if the existence of these particles is confirmed, it could open up a fertile field for more basic research and technological applications. Since Majorana fermions do not have charge, unlike electrons, they are more protected from external influences and could, in theory, be used as more stable platforms for the manipulation of their quantum states. Additionally, they would allow the performance of certain complicated computational operations that cannot be carried out with electrons. “But, of course, we have to find them first,” he jokes.
Majorana fermions in topological superconducting quantum wires and wells (nº 2012/20199-3); Grant Mechanism Grants in Brazil – Regular – Post-doctorate; Principal Investigator José Carlos Egues (IFSC-USP); Grant Recipient Edson Vernek; Investment R$ 170,950.58 (FAPESP).
VERNEK, E. et al. Subtle leakage of a Majorana mode into a quantum dot. Physical Review B. V. 89, 165.340. Apr. 30, 2014
HACHIYA, M. O. et al. Ballistic spin resonance in multisubband quantum wires. Physical Review B. V. 89, 125.510. Mar. 25, 2014