In my thesis I study Majorana fermions from three different perspectives. The first one corresponds to non-interacting Majorana fermions that, however, pose non-trivial topological properties. The... Show moreIn my thesis I study Majorana fermions from three different perspectives. The first one corresponds to non-interacting Majorana fermions that, however, pose non-trivial topological properties. The second one corresponds to strongly interacting Majoranas and the third to relic neutrinos. No one knows for sure if they have Dirac or Majorana nature. Show less
Majorana fermions in superconductors are the subgap quasiparticle excitations that are their own antiparticles.They occur on the boundary of so-called topological superconductors and are an equal... Show moreMajorana fermions in superconductors are the subgap quasiparticle excitations that are their own antiparticles.They occur on the boundary of so-called topological superconductors and are an equal weight quantum superposition of a positively charged electron and a negatively charged hole, that makes them charge-neutral but not an eigenstate of charge. Thus, the expectation value of charge vanishes, but the fluctuations of charge stay finite.Study of the latter ones would provide a purely electrical detection of Majorana states. In this thesis, we show that the electrical shot noise (the second moment of charge fluctuations) originated from the surface of a three-dimensional topological superconductor is related to the thermal conductance with a coefficient which consists of temperature and fundamental constants.The second part of the thesis is devoted to the strongly interacting fermionic zero modes (both Dirac and Majorana) described by the Sachdev-Ye-Kitaev model, which can be realized in disordered quantum dots in magnetic fields. The theoretical predictions of the spectroscopic properties of such quantum dots are presented in this thesis. Show less
