Majorana Fermions in Magnetic Chains

TL;DR

This paper reviews recent theoretical and experimental progress in realizing Majorana fermions in condensed matter systems, especially in magnetic impurity chains on superconductors, highlighting their potential for quantum computing.

Contribution

It provides a comprehensive overview of the theoretical foundations, experimental techniques, and evidence for Majorana fermions in topological superconductors, emphasizing magnetic chains.

Findings

Evidence of zero-bias peaks in tunneling experiments

Successful realization of synthetic topological superconductors

Identification of open questions for future research

Abstract

Majorana fermions have recently garnered a great attention outside the field of particle physics, in condensed matter physics. In contrast to their particle physics counterparts, Majorana fermions are zero energy, chargeless, spinless, composite quasiparticles, residing at the boundaries of so-called topological superconductors. Furthermore, in opposition to any particles in the standard model, Majorana fermions in solid-state systems obey non-Abelian exchange statistics that make them attractive candidates for decoherence-free implementations of quantum computers. In this review, we report on the recent advances to realize synthetic topological superconductors supporting Majorana fermions with an emphasis on chains of magnetic impurities on the surface of superconductors. After outlining the theoretical underpinning responsible for the formation of Majorana fermions, we report on the subsequent experimental efforts to build topological superconductors and the resulting evidence in favor of Majorana fermions, focusing on scanning tunneling microscopy and the hunt for zero-bias peaks in the measured current. We conclude by summarizing the open questions in the field and propose possible experimental measurements to answer them.