[Paper Review] Majorana quasiparticles in condensed matter

Ramón Aguado|arXiv (Cornell University)|Oct 31, 2017

Topological Materials and PhenomenaPhysics and Astronomy195 references301 citations

TL;DR

A survey of Majorana quasiparticles in condensed matter with emphasis on artificial one-dimensional topological superconductivity, BdG formalism, and experimental progress in nanowire and related platforms.

ABSTRACT

In the space of less than one decade, the search for Majorana quasiparticles in condensed matter has become one of the hottest topics in physics. The aim of this review is to provide a brief perspective of where we are with strong focus on artificial implementations of one-dimensional topological superconductivity. After a self-contained introduction and some technical parts, an overview of the current experimental status is given and some of the most successful experiments of the last few years are discussed in detail. These include the novel generation of ballistic InSb nanowire devices, epitaxial Al-InAs nanowires and Majorana boxes, high frequency experiments with proximitized quantum spin Hall insulators realised in HgTe quantum wells and recent experiments on ferromagnetic atomic chains on top of superconducting surfaces.

Motivation & Objective

• Explain Majorana quasiparticles and their relation to superconductivity and particle-hole symmetry.
• Survey theoretical frameworks leading to 1D topological superconductivity (Kitaev chain, Rashba systems, Fu–Kane model).
• Review experimental implementations and detection protocols for Majorana zero modes in engineered platforms.
• Summarize recent experimental progress in semiconducting nanowires, epitaxial superconductor–semiconductor hybrids, and related systems.

Proposed method

• Present a self-contained introduction to Dirac and Majorana concepts.
• Describe the Bogoliubov–de Gennes formalism and its relation to Majorana physics.
• Discuss canonical models (chiral p+ip and Kitaev) and non-Abelian braiding concepts.
• Outline two main artificial implementations: Fu–Kane topological insulator proximity and Rashba semiconductor platforms.
• Detail experimental detection protocols (e.g., quantized conductance, 4π Josephson effect, Coulomb blockade in Majorana islands).
• Review progress in induced one-dimensional topological superconductivity across multiple platforms.

Experimental results

Research questions

• RQ1 How can Majorana zero modes be realized in condensed matter systems through artificial topological superconductivity?
• RQ2 What are the theoretical connections between BdG quasiparticles and Majorana fermions in superconductors?
• RQ3 What experimental platforms provide the most compelling evidence for Majorana modes and how are they detected?
• RQ4 What are the principal experimental challenges and milestones in one-dimensional Majorana platforms such as semiconducting nanowires and topological-insulator edges?
• RQ5 How do different material architectures (e.g., InSb, Al–InAs, HgTe, atomic chains) contribute to advancing Majorana detection and manipulation?

Key findings

• The BdG framework inherently provides particle–hole symmetry that links superconducting quasiparticles to Majorana fermions.
• Majorana zero modes arise at zero energy in topological superconductors and are robust to perturbations that do not close the gap.
• Two canonical routes to artificial Majorana platforms are the Fu–Kane topological insulator proximity setup and Rashba-based semiconductor systems with induced p-wave pairing.
• A range of experimental detection protocols exists, including normal metal–superconductor transport signatures, 4π Josephson effects, and Coulomb blockade phenomena in Majorana islands.
• Recent experimental progress spans ballistic InSb nanowires, epitaxial Al–InAs nanowires with Majorana modes, Majorana boxes, proximitized quantum spin Hall edges in HgTe wells, and ferromagnetic atomic chains on superconductors.
• Despite significant advances, unambiguous evidence of non-Abelian braiding and topological superconductivity remains challenging, with ongoing efforts across multiple platforms.