What is the order of magnitude of the energy released in Majorana fermions collision/annihilation?

Majorana fermion experiment

It has been observed a quantum state in a one atom thick wire which in a certain energy range behaves like a Majorana fermion. It is a quasiparticle that arises out of the collective behavior of the electrons in superconducting materials. It is probably related to the simulation of the 1D Majorana equation with two Cooper pairs coupled to a 1D superconducting transmission line resonator, where the strong coupling limit can be achieved (see the link above).

What is the effective mass of the Majorana fermion?

If the wire is sufficiently long, the emerging Majorana fermions do not annihilate, and are stable. For certain ranges of the wire length, the newly formed Majorana fermions can annihilate.

What is the order of magnitude of the energy released in the Majorana fermions annihilation? Is it anywhere around 4mc^2 (where m is the electron mass), at least as order of magnitude (this is a guess)?

How does this energy compare with the total energy input assumed in the experiment (for one wire), in order to create these quasiparticles? Can the system be scaled up, for the purpose of energy production (many wires that cyclically host annihilation processes)? Could the phenomenon appear in higher temperature superconductors (in order to decrease the necessary energy input)?

• The energy released by annihilation at rest would be the mass energy, so the question is in effect asking for the mass of the particular quasiparticle you're interested in. (BTW "Majorana fermion" describes a class of particles that have certain symmetries, not a particular particle (quasi- or otherwise); the title might be better addressing the particular state you are interested in rather than a whole class that includes things like standard-model neutrinos.) Jul 29, 2017 at 19:00

First of all the notion of fermion here is kinda sketchy, Majorana zero modes are really neither a fermion nor a boson but an anyon - see https://arxiv.org/pdf/1907.06497.pdf for a good overview on this. Second of all Majoranas in particle physics and condensed matter are quite a different thing so:

What is the effective mass of the Majorana fermion?

In realistic models, Majorana Bound States (MBS) are quasiparticles, not a real particles like fermionic electrons are. In this case MBSs emerge from combined behavior of all of the electrons in nanowire. Therefore, mass is an ill-defined concept.

What is the order of magnitude of the energy released in the Majorana fermions annihilation?

Majorana quasiparticles do not possess energy (hence the "Zero energy bias peak") if they are of anyonic nature, so annihilation would give 0 as well. Their annihilation is just a familiar (yet kinda misleading) name, in reality its just a destructive interference.

How does this energy compare with the total energy input assumed in the experiment (for one wire), in order to create these quasiparticles?

Its not really a question of energy transfer but of fine-tuning the ingredients. When you change the magnetic field up until the transition to topologically non-trivial state (where MBS can appear) you change the energy of each state but the net is still 0. This is because the energy you put into system (for example with external magnetic field) does not just create particle excitations but closes the superconducting gap allowing for two states to degenerate at zero energy. Then you just supply 0 energy to the system and excite MBS there, at those degenerate states.

Can the system be scaled up ?

That is the Nobel prize question - Scalable Majorana systems could pave way for fault-free quantum computing. As for the energy production (did you mean transformation?) I haven't seen any proposal that would make sense. Yes, this could happen in HTSC but those are poorly understood (in comparison with type 1 superconductors) and there is plenty other phenomena to rule out so small temperatures are beneficial (but really mandatory) for research.