Majoranas

Majoranas refers to Majorana fermions, particles that are their own antiparticles. In particle physics, a Majorana fermion would be a real solution to the Dirac equation. The concept was introduced by Ettore Majorana in 1937. Unlike Dirac fermions such as electrons, a Majorana particle has no distinct antiparticle.

In condensed matter physics, Majorana modes can appear as zero-energy bound states in topological superconductors. These Majorana bound states are emergent quasiparticles that are their own antiparticles and are spatially localized, for example at the ends of a one-dimensional topological superconductor or at vortices in two-dimensional superconductors. They are described by non-Abelian statistics, meaning exchanging two such modes changes the ground state in a way that depends on the order of exchanges, enabling topologically protected quantum operations.

Proposed realizations include semiconductor nanowires with strong spin-orbit coupling in proximity to an s-wave superconductor, under a magnetic field; two-dimensional systems such as topological insulators with superconducting pairing; and iron-based superconductors with intrinsic topological surface states.

Experimental evidence has included zero-bias conductance peaks in tunneling spectroscopy compatible with Majorana bound states, observed in InSb or InAs nanowires with aluminum, and in some iron-based superconductors. However, alternative explanations and disorder effects complicate interpretation, and as of now there is no universally accepted demonstration of non-Abelian Majorana statistics.

If realized and controllable, Majorana modes could form the basis of fault-tolerant topological quantum computing, using nonlocal qubits protected from local noise and quantum gates implemented by braiding.