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

Abstract

Ettore Majorana (1906Majorana ( -1938 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 anti-particle. 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 spin-1 2 neutral particles that may be truly neutral with no quantum number to distinguish them from their anti-particles. If such particles exist, they will influence many areas of nuclear and particle physics. Most notably the process of neutrinoless double beta decay can only exist if neutrinos are massive Majorana particles. Hence, many efforts to search for this process are underway. Majorana's influence doesn't stop with particle physics, however, even though that was his original consideration. The equations he derived also arise in solid state 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 review 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 anti-particle in nuclear, particle, and solid state physics.

Z3 Parafermionic Zero Modes without Andreev Backscattering from the 2/3 Fractional Quantum Hall State

“…This surge of interest can be largely attributed to potential application of such systems as building blocks for topological quantum computers [1]. Majorana zero modes (MZMs) [2][3][4][5][6][7] provide the simplest and experimentally the most promising example of non-Abelian anyons. So far, most of the effort in searching for non-Abelian anyons has been focused on MZMs.…”

Dirac open-quantum-system dynamics: Formulations and simulations

“…Partial robustness was also observed for a coordinate dependent mass term in the Dirac equation. This robustness represents yet another remarkable attribute of Majorana spinors [122] not presently acknowledged, which may be important experimentally. Moreover, the dynamics of the Klein paradox as well as Klein tunneling turned out to be weakly affected by quantum dephasing.…”

Quantum upside-down cake

“…The evidence is indirect because it cannot rule out the possibility that non-chiral edge modes are responsible for the observed X-shaped gap boundaries. If the chiral character of the edge modes is confirmed, the authors' system might be an excellent platform for studying Majorana states, which are of interest, not only for topological quantum computation, but also in elementary-particle physics 10 …”