The Majorana Fermions

Story start with discovery of antiparticle (Positron) by Dirac by an attempt to unified  Theory of relativity and Quantum mechanics. 1932 positron was discovered in 192 in cosmic ray. Dirac equation describe charged spin 1/2 Fermions.
In 1937 Majorana predicted one new type of perticle by smartly choosing  gamma matrices of Diraction so that the wave function of the particle is real and then this particle will be self conjugate. But don't forgate it is still a spin 1/2 Fermion !! Waoo.. that.s amazing a charge neutral, spin1/2, self conjugate (a particle with it's own anti particle) Fermion.

In condensed matter there is findings of Majorana Bound state on the boundary of a 1D topological supercoductor  (0+1) that are localize not propagating

Edge of a 1D superconductor :

https://arxiv.org/abs/cond-mat/0010440

If in a 1D wire,in the middle there is no state but there is at the end. Now if it has a state in positive side then it should have it’s partner in negative side. But this not true for  the is zero energy state at the end and it  don’t have any partner. Now this state we can’t get rid of it.It is topologically protected. If we try to move it away then the partner could be nowhere to be found. Now adding a particle in this zero energy state is equivalent to removing the same from this zero energy state!! So this zero energy particle is it’s antiparticle means it’s half of it’s particle. Called Majorana particle.

http://iopscience.iop.org/article/10.1070/1063-7869/44/10S/S29/meta
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.177002
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.105.077001
Expt. from Yazdani group in Prince ton:
http://science.sciencemag.org/content/346/6209/602
http://science.sciencemag.org/content/336/6084/1003

Majorana Bound states in vortex of a 2D topological superconductor:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.104.040502
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.100.096407
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.81.125318
expt:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.116.257003

Latter found propagating Majorana Fermions in chiral topological super conductor by sandwich of quantum anomalous hall insualtor and a superconductor.

https://journals.aps.org/prb/abstract/10.1103/PhysRevB.82.184516
 proposal of detecting majorana by transport measurement: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.83.100512
https://journals.aps.org/prb/abstract/10.1103/PhysRevB.92.064520

A majorana fermion can be imgined as half of Dirac electron. So it will show hall conductance  will be half of normal electron quantum hall conductance !!
Expt. Observation by S.C. Zhang idea:
http://science.sciencemag.org/content/357/6348/294

Well the experiment has been objected by many group and claimed the observed effect could be because of quantum decoherence.

https://www.condmatjclub.org/uploads/2017/09/JCCM_September_2017_01.pdf
https://arxiv.org/abs/1708.06214
https://arxiv.org/abs/1708.06752

Here is the reply that the observed effect is real by  .C.Zhang Stanford
https://arxiv.org/abs/1709.05558

There is alternate suggestion of expt.:
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.216403
https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.102.216404