The building-blocks of matter — protons, neutrons and electrons — are examples of particles called fermions. Eight decades ago, the Italian physicist Ettore Majorana predicted the existence of fermions that are their own antiparticles1. These particles, now known as Majorana fermions, would be of great fundamental interest, and could revolutionize quantum computing. Evidence for Majorana fermions among elementary particles remains elusive; however, in the past few years, there has been striking progress in this hunt in the realm of condensed-matter physics2. In two papers in Nature, Banerjee et al.3 and Kasahara et al.4 report signatures of Majorana fermions in heat-transport experiments in two very different condensed-matter settings.
Condensed-matter systems contain excitations that behave like ordinary particles, but that need not resemble the actual elementary particles that the systems are made of. For example, the phenomenon of superconductivity (more specifically, topological superconductivity) provides a setting in which an electron can effectively ‘forget’ its electric charge. As a result, the electron becomes indistinguishable from its antiparticle, which in this context is an electron vacancy called a hole. Whether topological superconductivity is an intrinsic feature of solid-state materials remains an open question. However, the key aspects of the phenomenon can be mimicked in certain condensed-matter systems, providing the right conditions for the emergence of Majorana fermions. The two systems investigated in the current papers seem to be of just this kind.
Banerjee and colleagues looked for evidence of Majorana fermions on the edge of a condensed-matter system that exhibits the quantum Hall effect — whereby, at low temperature and in the presence of a strong magnetic field, the material’s transverse electrical conductance becomes quantized (it can have only specific values). The authors focused on a particular state for which this conductance is 5/2 times the fundamental unit. The exact nature of this state has been a subject of debate, but all of the strong contenders can be thought of as superconducting states of composite fermions5.
By contrast, Kasahara and colleagues investigated a form of ruthenium chloride known as α-RuCl3. This material is thought to be in a phase known as the Kitaev spin liquid — a peculiar state of matter that lacks long-range magnetic order all the way down to zero kelvin6,7. Although α-RuCl3 is an electrical insulator, the description of the magnetic properties of a Kitaev spin liquid is mathematically equivalent to that of a topological superconductor. Therefore, Majorana fermions should exist on the edge of α-RuCl3.
The direct detection of Majorana fermions in condensed-matter systems was never going to be easy. Such particles must be electrically neutral and therefore cannot participate in electrical transport (although they can mediate such transport in superconductors8,9). However, although Majorana fermions are unable to conduct current, they can conduct heat.
Electrons can conduct both electricity and heat. As a result, metals — which contain many free electrons — are typically good heat conductors. This idea is formalized by the Wiedemann–Franz law, which states that electrical conductivity is directly proportional to thermal conductivity divided by temperature. Although the identification of this relationship is often lauded as one of the early successes of solid-state theory, the proportionality constant is not universal for ordinary metals: scattering processes, which limit both electrical and thermal conductivity, affect these properties differently in different metals.
However, if the motion of particles in a material is ballistic (if there is effectively no scattering), both electrical and thermal conductivity are quantized and proportional to the number of propagating modes (conduction channels). Each electron mode contributes a unit of thermal conductance, and, crucially, each Majorana mode contributes only half a unit. Both Banerjee et al. and Kasahara et al. observed this fraction of thermal conductance on the edges of their condensed-matter systems.
The existence of Majorana edge modes in a condensed-matter system is a strong indicator that the topological order of the system is non-Abelian — which means, for example, that a collection of the system’s excitations has a huge number of quantum states with the same energy. The non-Abelian nature of the quantum Hall state studied by Banerjee et al. has long been expected (albeit not confirmed beyond reasonable doubt). However, Kasahara and colleagues’ findings provide the first experimental evidence of a non-Abelian spin liquid. Although more work is needed to confirm the exact nature of this state, the discovery of such an unconventional phase of matter is truly exciting.
Banerjee and colleagues used their measurements to try to discriminate between different candidate non-Abelian states. This task is harder than obtaining evidence for non-Abelian topological order. It relies on counting both fractional and integer contributions to the system’s thermal conductance, which, in turn, requires certain assumptions to be made about the process by which different propagating modes reach thermal equilibrium10. The issue of equilibration is further complicated by the fact that the edge modes can reach equilibrium not only with each other, but also with lattice vibrations called phonons, which provide an unwanted contribution to the thermal conductance.
Banerjee et al. went to great lengths to minimize this phonon contribution. They carried out their experiments at temperatures of about 20 mK and used a sophisticated design of a source and drains to avoid the coupling of edge modes to phonons. By comparison, Kasahara and colleagues’ experiment was much less intricate and required temperatures of only about 5 K. These authors could not detect a signal of half-integer quantization at lower temperatures, which probably suggests that the system transitioned to a different phase. Their results also indicate that a substantial amount of heat was carried by phonons.
Under these circumstances, it should be surprising that the authors saw signs of quantized Hall heat transport — the heat conduction in the direction perpendicular to that of the thermal gradient — by Majorana fermions. However, two recent studies11,12 have argued that phonon coupling not only is not detrimental, but also can actually be necessary for the observation of such an effect. More work, both theoretical and experimental, is required to fully understand the implications of these experiments. Nevertheless, it is undoubtedly exciting that the quest for Majorana fermions is heating up in this manner.
Nature 559, 189-190 (2018)