Colloquium : Majorana fermions in nuclear, particle, and solid-state physics

In nature one can associate to each particle an antiparticle with equal mass and opposite charge: to the electron there is the positron, to the proton there is an anti-proton, etc. Majorana fermions are particles with an identity crisis: they are their own antiparticles and hence they self-annihilate. In this Colloquium the nature of Majorana particles and their presence in several different branches of physics is discussed from nuclear to condensed matter. Ettore Majorana (1906-1938) disappeared while traveling by ship from Palermo to Naples in 1938. Most notably the process of neutrino-less double beta decay can exist only if neutrinos are massive Majorana particles. Hence, many efforts to search for this process are underway. The equations he derived also arise in solid-state physics where they describe electronic states in materials with super-conducting order. This Colloquium first summarizes the basics of Majorana's theory and its implications. It then provides an overview of the rich experimental programs trying to find a fermion that is its own antiparticle in nuclear, particle, and solid-state physics.