thesis In search of Majorana

Paul Dirac’s famous equation, which he first But even if the neutrino turns out not to wrote down in January of 1928, predicted Quite a flowering be a Majorana particle, the mathematical the existence of a spin-1/2 particle and a of results has come idea still holds weight. Indeed, the corresponding antiparticle. The ensuing Majorana equation (as originally derived experimental discovery of the positron, the from Majorana’s short from the Dirac equation) arises naturally antiparticle of the electron, served to boost mathematical insight in the description of electrons in solids the theory. Dirac’s equation helped establish with superconducting order. Here, a basis for relativistic quantum field theory. into Dirac’s equation. these excitations appear as electrically But the equation had been studied for neutral quasiparticles — fermions with a full ten years before Italian physicist case, as a charge-free spin-1/2 solution no distinction between particles and Ettore Majorana noticed an interesting of Dirac’s equation. For a charged Dirac antiparticles. The ordinary superconducting special case. The equation is really four particle, the operation of charge conjugation energy gap — the energy required to coupled equations, one for each component changes a particle into its antiparticle. create such an excitation — plays the of the Dirac field. If one demands that the The same operation turns the Majorana role of the Majorana mass. In this sense, solution be real, rather than complex, the solution into itself. Majorana particles appear routinely in equation resolves itself into two independent Of the fundamental particles we know, physics laboratories. pairs of equations, each pair describing a the neutrino seems to be the best Majorana Far more interesting, as Elliott and spin-1/2 particle, but now with no charge. candidate. It’s a neutral spin-1/2 fermion. Franz describe, are some special cases of The particle is its own antiparticle; clearly Left-handed neutrinos have a very small Majorana modes that can exist in topological not like an electron or positron. mass (if any), and right-handed ones have superconductors in one or two dimensions. Nearly a century later, we’re still not never been detected, suggesting they have a These modes are localized around defects, sure that Majorana’s hypothetical particle very large mass. Simple models of particle always come in pairs (in any finite system), is definitively like any real world object. physics suggest this should actually be possess exactly zero energy and are His fermion stands as a great expectation expected if neutrinos are Majorana fermions. known as Majorana zero modes. If the and possibility. Majorana himself suggested Majorana status for neutrinos would also superconductor has the usual energy gap, that the neutrino may be such a particle, make a tidy accounting for a number of deep then such ground states have an unusual and many physicists think as much. This physics puzzles. It would help to explain ‘topological protection’ — they are robust would help unravel a number of mysteries, the great imbalance between matter and to perturbations, as the system lacks any including why there’s a vast asymmetry antimatter in the universe, as weak processes mechanism for absorbing small amounts between matter and antimatter. But, we still involving Majorana neutrinos can violate of energy. don’t know. otherwise sacrosanct conservation laws, in These states have now been observed Even so, it seems that Majorana’s particular, allowing changes in the lepton in the ends of one-dimensional mathematical idea has become more number and also in the baryon number, superconducting wires, and also in the influential than ever in the past decade, leading to an imbalance of matter and vortex cores of two-dimensional topological impacting areas across all physics. antimatter over time. Majorana status for the superconductors. Over a decade ago, As physicists Steven Elliott and neutrino could also fill out the theoretical Alexei Kitaev proposed that the protected Marcel Franz discuss in a recent review idea of supersymmetry, as well as help settle status of these states might make them (Rev. Mod. Phys. 87, 137; 2015), precise the mystery of dark matter. useful for quantum computing if qubits analogues of the Majorana fermion do exist But convenient implications aren’t the could be formed from pairs of defects. in condensed-matter physics. The inside of same as evidence. Confirming that neutrinos Logical operations could be carried out by a superconductor is, in effect, a universe of really are Majorana particles will require moving the defects around one another. its own, and one that supports quasiparticle actual detection of one or more signature That goal still seems a long way away, but excitations of exactly the Majorana form. events. Any observation of a decaying these Majorana states do possess intrinsically In one- or two-dimensional systems, proton would suffice, as would any process promising properties. Majorana-like modes can take on unusual in which the lepton number changes by two. All in all, quite a flowering of results properties, and might even be useful in There are ongoing searches in accelerator from Majorana’s short mathematical insight quantum computing. Weirdly, Majorana’s experiments, but no evidence yet. Another into Dirac’s equation. He studied under idea may find fruitful use in technology even signature would be the observation of so- Enrico Fermi in Rome, later worked for a before true Majorana particles are discovered called neutrino-less double beta decay — a time with Heisenberg, and published nine anywhere in the universe. decay in which a nucleus emits two electrons papers. He then disappeared mysteriously To a theoretical physicist, ‘particle’ is a and no neutrinos. This has also never been while travelling on a boat from Palermo versatile term. It can mean the real physical seen, but the rate of such decays is expected to Naples in 1938. No one knows what thing, carrying mass, charge and other to be small, as it should be proportional happened; some reports suggest he was properties. Or, it can be a possibility — a to the neutrino mass. Ever more precise later seen in Venezuela after the war. His specific way for energy and momentum to experiments have now bounded the neutrino fate remains as enigmatic as the Majorana exist as an elementary excitation in a system mass to be no more than about 200 meV; neutrino itself. ❐ described by a particular set of equations. experiments underway will be sensitive The Majorana fermion falls into the latter down to 50 meV. MARK BUCHANAN

206 NATURE PHYSICS | VOL 11 | MARCH 2015 | www.nature.com/naturephysics

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