New directions in the pursuit of Majorana fermions in solid state systems

TLDR

Majorana fermions, first theorized in 1937, have influenced fields from neutrino physics to superconductivity, yet their unambiguous detection remains an outstanding challenge. This review surveys recent progress in the condensed‑matter search for Majorana modes, arguing that the field is approaching a breakthrough and addressing how they can be experimentally identified. The authors describe how topological one‑ and two‑dimensional superconductors—realized by engineering heterostructures with ordinary s‑wave superconductors—support Majorana bound states at edges and vortices, and they review tunneling, Josephson, and interferometric measurements as definitive signatures. They highlight that Majorana excitations exhibit non‑Abelian exchange statistics, offering a platform for fault‑tolerant quantum computation.

Abstract

The 1937 theoretical discovery of Majorana fermions--whose defining property is that they are their own anti-particles--has since impacted diverse problems ranging from neutrino physics and dark matter searches to the fractional quantum Hall effect and superconductivity. Despite this long history the unambiguous observation of Majorana fermions nevertheless remains an outstanding goal. This review article highlights recent advances in the condensed matter search for Majorana that have led many in the field to believe that this quest may soon bear fruit. We begin by introducing in some detail exotic `topological' one- and two-dimensional superconductors that support Majorana fermions at their boundaries and at vortices. We then turn to one of the key insights that arose during the past few years; namely, that it is possible to `engineer' such exotic superconductors in the laboratory by forming appropriate heterostructures with ordinary s-wave superconductors. Numerous proposals of this type are discussed, based on diverse materials such as topological insulators, conventional semiconductors, ferromagnetic metals, and many others. The all-important question of how one experimentally detects Majorana fermions in these setups is then addressed. We focus on three classes of measurements that provide smoking-gun Majorana signatures: tunneling, Josephson effects, and interferometry. Finally, we discuss the most remarkable properties of condensed matter Majorana fermions--the non-Abelian exchange statistics that they generate and their associated potential for quantum computation.