Signatures of Majorana Fermions in Hybrid Superconductor-Semiconductor Nanowire Devices
Authors: Vincent Mourik1, Kun Zuo1, Sergey Frolov1, Sébastien Plissard2, Erik Bakkers1,2, Leo Kouwenhoven1
1Kavli Institute of Nanoscience, Delft University of Technology, Netherlands.
2Dept of Applied Physics, Eindhoven University of Technology, Netherlands.
Paul Dirac was the very first particle predictor. In 1927, Dirac developed a formula that linked two new theories: Einstein’s special theory of relativity and quantum mechanics. Dirac’s equation, however, had several solutions. The first solution described the familiar electron: a particle with a negative charge holding a certain amount of positive energy. Another solution actually constituted its very opposite: a positively charged particle holding a certain amount of negative energy. Rather than ignoring the contradiction raised by his additional solution, Dirac surmised that there must be a particle in nature with a positive electrical charge and negative energy . This particle therefore has properties that would exactly mirror the properties of an electron. Several years later, this particle was indeed found, and was named positron. Together, the electron and the positron form a particle and antiparticle pair.
A pure genius, Paul Dirac was utterly convinced of the veracity of his formula. If his equation offered a certain solution, then a corresponding particle simply had to exist in nature. Since that time, numerous other particles have been predicted and identified this way. For example, the ongoing search for the Higgs boson is set up just like that, based on a prediction from the Standard Model.
For decades the Majorana particle received little attention, but in the 1970s the search began afresh. Using large accelerators and detectors, scientists started hunting for neutrino particles with Majorana properties. Indeed, these elementary Majorana particles might even solve the mystery of dark matter that fills our Universe. So far, the elementary Majorana particles have remained elusive, but this important quest is still being pursued by CERN in Geneva.
In addition to elementary particles, composite or collective particles (see box) also exist in the world of condensed matter physics. We know of heat particles (phonons), electron density waves (plasmons), magnetic waves (magnons) and a long list of other collective particles. These collective particles are particularly convenient for making the physics of materials a lot simpler. Materials hold a distinct place in physics because by combining materials we can create objects that did not exist before. Technology, for instance, abounds with remarkable material combinations, such as silicon and silicon oxide forming the backbone of electronics. But material combinations can also be used in fundamental physics to create something new. This prompted a number of theoretical physicists to reflect on whether we could combine materials in such a way that the collective particles inside them will acquire the properties of Majorana fermions.
The one-dimensional lattice proposed by Alexei Kitaev in 2001 was still highly mathematical and abstract . A number of propositions then followed based on (p-wave superconducting) materials that did not yet exist. In 2008, Liang Fu and Charles Kane’s theory  was the first to be based on existing materials, but was still difficult to put into practice. The year 2010 saw the publication, in Physical Review Letters of two similar theories by two groups of theorists, independently of each other, which for the first time looked feasible in practice. One of the publications  came from theorists at the University of Maryland (Roman Lutchyn, Jay Sau and Sankar Das Sarma); the other  was a collaborative effort between theorists at the Weizmann Institute in Israel, California Institute of Technology of USA and the Free University of Berlin in Germany (Yuval Oreg, Gil Rafael and Felix von Oppen). The importance of the aforementioned theoretical developments was that it shifted the focus from what is found in nature to the artificial creation of Majorana particles.
The Majorana fermions in crystals are not only interesting from a fundamental viewpoint, but also have unique properties that can be used to build a quantum computer. Field medalist Michael Freedman works at Microsoft and has been carrying out active research into topological quantum computers with a team of scientists since 2005. This computer works by moving Majorana particles around each other and forming space-time braids.
The proposals put forward by Lutchyn et al  and Oreg et al  are both based on bringing semiconducting nanowires into contact with a superconducting material. We had already successfully accomplished this combination in Delft, which resulted in publications in Science (2005) and Nature (2006). Combining these specific materials suddenly made us the experimental specialists in the search for Majorana fermions.
Note that the Majorana quest had already been described at an early stage in the journal 'Science' .
Majorana in Delft:
In this device, the superconductor is larger than the semiconductor. The diameter of the nanowire is so small that it actually becomes a one-dimensional conductor. A portion of the superconductor is covering the nanowire, which causes the superconductivity to leak into the semiconductor, effectively creating a one-dimensional superconductor. These do not exist in nature but can be induced this way. The strong spin-orbit coupling in the InSb nanowire makes this one-dimensional superconductor particularly unique. It has a so-called p-symmetry, which again has also not been found in nature. This p-superconductor extends across the entire section where the nanowire is in contact with the superconductor. At the end points, where the p-superconductor ends, two Majorana fermions appear, one on each end point.
Image: The microchip used with three different Majorana devices. This chip is cooled down to almost absolute zero point (-273 degrees Celsius). The electrical wires are connected to measuring equipment at room temperature.
We can measure the Majorana fermions in the electrical conductivity. From the gold contact we send electrons into the nanowire, towards the lower Majorana fermion. Only when we send electrons inside with precisely zero energy can we measure a current. If we add voltage to the electrons to energise them further, they are reflected at the p-superconductor and we measure zero conductivity. The presence of the Majorana fermion in our system is therefore visible as a conductance peak at a voltage that is precisely zero.
In the 'Science' publication  we also included various control experiments, which demonstrate that each single ingredient from the original theory is essential for this observation. The results can only be interpreted if we assume the presence of Majorana fermions. The article is published online on 12 April in 'Science Express' .
Image: The nanowire, shown vertically in this photo, is lying flat on a substrate. Hidden in the substrate are different gate electrodes (the horizontal ‘stripes’ below the nanowire and the contacts), which can change the conductivity of the nanowire. The lower electrical contact to the nanowire is madefrom gold, a normal conductor. The contact on the top is covering half of the nanowire. This is the superconductor. The total length of the nanowire is three micrometres. The anticipated positions of two Majorana fermions are indicated with red stars.
We have since been carrying out new experiments. As the title of our article ‘Signatures of …’ suggests, we also want to demonstrate other unique properties of Majorana fermions. And our Majorana fermions are literally one of a kind. Nature has two types of particles: fermions (such as electrons, positrons, neutrons, etc.) and bosons (photons, Higgs particles, phonons, etc.). Our Majorana particles are likely to have other properties than fermions and bosons. In terms of physics, their behaviour is described by non-Abelian statistics. If we can demonstrate these statistics in our new experiments, we add a completely new chapter to the book of physics. This new round of experiments is based on a highly theoretical approach using new concepts that are not yet quite understood. To translate abstract concepts into experiments we are working with Carlo Beenakker’s theory group from Leiden. The non-Abelian statistics also make Majorana particles useful for a topological quantum computer.
 P. A. M. Dirac, "The Quantum Theory of the Electron". Proceedings of the Royal Society of London: Series A 117, 610–624 (1928). Full Article.
 Ettore Majorana, "Teoria simmetrica dell’elettrone e del positrone", Il Nuovo Cimento, 171 (1937). Abstract.
 A. Yu. Kitaev, "Unpaired Majorana fermions in quantum wires". Physics Uspekhi, 44, 131 (2001). Full Article.
 Liang Fu and Charles Kane, "Superconducting Proximity Effect and Majorana Fermions at the Surface of a Topological Insulator", Phys. Rev. Lett. 100, 096407 (2008). Abstract.
 Roman M. Lutchyn, Jay D. Sau and Sankar Das Sarma, "Majorana Fermions and a Topological Phase Transition in Semiconductor-Superconductor Heterostructures", Physical Review Letters, 105, 077001 (2010). Abstract.
 Yuval Oreg, Gil Refael, and Felix von Oppen, "Helical Liquids and Majorana Bound States in Quantum Wires", Physical Review Letters, 105, 177002 (2010). Abstract.
 Robert F. Service, "Search for Majorana Fermions Nearing Success at Last?", Science, 332, 193 (2011). Abstract.
 V. Mourik, K. Zuo, S.M. Frolov, S.R. Plissard, E.P.A.M. Bakkers, L.P. Kouwenhoven, "Signatures of Majorana fermions in hybrid superconductor-semiconductor nanowire devices", Science Express, DOI: 10.1126/science.1222360 (Published Online April 12 2012). Abstract.