FERMIONS Doubling down on Majorana

Ettore Majorana has been missing for 74 years, but his most important legacy in physics is lately very much in the news. The still-hypothetical Majorana fermion is in a sense a completely ‘real’ particle — its mathematical representation doesn’t have an imaginary part — it is, therefore, its own antiparticle. Whereas particle physics was the context of the original proposal — and experiments aiming to test whether the neutrino is a Majorana fermion are ongoing — the search for this elusive structure is hottest in condensedmatter physics. In the solid state, a single conventional (or Dirac) fermion is equivalent to a pair of Majorana fermions: all we need is a way to split the pair1. Leonid Rokhinson and his co-workers, as they describe in Nature Physics2, have now observed an important hint of such splitting in a semiconductor nanowire with superconducting contacts. Among a spate of theoretical recipes for spatially separating Majorana fermions, two have caught the eye of experimentalists for their apparent ease of implementation: join a conventional superconductor (like aluminium or niobium) to either a material with strong spin–orbit coupling3,4 or a topological insulator5 and measure. But what should we measure to detect a ‘Majorana’? Two simple equations dictate how current flows between two superconducting leads separated by a conventional material — an arrangement known as a Josephson junction after Nobel-Prize winner Brian Josephson. First, the supercurrent, IS, evolves sinusoidally with the phase difference φ between the two superconducting wavefunctions across the junction: IS = ICsin(φ), where IC is the critical current. This is the d.c. Josephson effect. Second, a voltage V across the junction causes φ to oscillate with a frequency f = qV/h (the a.c. Josephson effect), where q is the charge of the carriers responsible for carrying supercurrent through the junction6. These carriers are generally pairs of electrons, therefore the corresponding charge is 2e. Taken together, these two Josephson relations imply that a voltage oscillating at a frequency matched to the junction frequency drives a d.c. current through the junction. A current– voltage measurement thus shows a set of ‘Shapiro steps’ at multiples of the voltage associated with the excitation frequency (V = hf/2e, solid line in Fig. 1a), typically in the microwave regime. It has been predicted7,8 that some junction materials will not follow the conventional relation IS = ICsin(φ) but will instead support a current that oscillates at twice the period in the junction phase: ICsin(φ/2). A voltage applied to such a junction will produce a characteristic frequency half that of normal junctions and a corresponding doubling in Shapiro step size: hf/e (dashed line in Fig. 1a). The doubling of the characteristic voltage spacing implies that individual electrons — resulting from the recombination of split Majorana-fermion pairs — are responsible for the tunnelling process. Majorana fermions only emerge from electrons when an ordinarily present degeneracy is broken; that is, when states with spin up no longer have an equivalent state with spin down. For a junction created from a nanowire with strong spin–orbit coupling, this condition can be satisfied by applying a magnetic field along the wire. In the absence of a magnetic field (Fig. 1b), at any energy where they exist, the mobile electrons come in all combinations of spin-up (blue) or spin-down (red) and right-moving (upward-sloped) or left-moving (downwardsloped). Applying a magnetic field removes the crossing of the spin-up and spin-down curves, so that if the Fermi energy, EF, is tuned close to the former crossing (Fig.1c) only right-movers with spin up and leftmovers with spin down are present, creating a ‘helical’ conductor9. Add a superconductor to the mix and the conditions necessary for the creation of Majorana fermions are satisfied3,4. Note that when this occurs and Majorana fermions are present in the junction, there should be a transition from the conventional Josephson relation to an unconventional one — IS ∝ sin(φ) → IS ∝ sin(φ/2) — and the characteristic voltage in the a.c. Josephson effect should be doubled. Rokhinson et al. measure the a.c. Josephson effect as a function of magnetic field in just such a system2. Their Josephson junction comprises two superconducting niobium leads bridged by a nanowire etched MAJORANA FERMIONS