Colloquium: Majorana fermions in nuclear, particle, and solidstate physics
Abstract
Ettore Majorana (19061938) disappeared while traveling by ship from Palermo to Naples in 1938. His fate has never been fully resolved and several articles have been written that explore the mystery itself. His demise intrigues us still today because of his seminal work, published the previous year, that established symmetric solutions to the Dirac equation that describe a fermionic particle that is its own antiparticle. This work has long had a significant impact in neutrino physics, where this fundamental question regarding the particle remains unanswered. But the formalism he developed has found many uses as there are now a number of candidate spin1 /2 neutral particles that may be truly neutral with no quantum number to distinguish them from their antiparticles. If such particles exist, they will influence many areas of nuclear and particle physics. Most notably the process of neutrinoless double beta decay can exist only if neutrinos are massive Majorana particles. Hence, many efforts to search for this process are underway. Majorana's influence does not stop with particle physics, however, even though that was his original consideration. The equations he derived also arise in solidstate physics where they describe electronic states in materials with superconducting order. Of special interest here is the class of solutions of the Majorana equation in one and two spatial dimensions at exactly zero energy. These Majorana zero modes are endowed with some remarkable physical properties that may lead to advances in quantum computing and, in fact, there is evidence that they have been experimentally observed. 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 solidstate physics.
 Publication:

Reviews of Modern Physics
 Pub Date:
 January 2015
 DOI:
 10.1103/RevModPhys.87.137
 arXiv:
 arXiv:1403.4976
 Bibcode:
 2015RvMP...87..137E
 Keywords:

 71.10.Pm;
 14.80.Va;
 Fermions in reduced dimensions;
 Condensed Matter  Superconductivity;
 Condensed Matter  Mesoscale and Nanoscale Physics;
 High Energy Physics  Experiment;
 Nuclear Experiment
 EPrint:
 Invited review for Reviews of Modern Physics