Synthesis of Majorana mass terms in low-energy quantum systems

Abstract

We discuss the problem of how Majorana mass terms can be generated in low-energy systems. We show that, while these terms imply the Majorana condition, the opposite is not always true when more than one flavour is involved. This is an important aspect for the low-energy realizations of the Majorana mass terms exploiting superfluid pairings, because in this case the Majorana condition is not implemented in the spinor space, but in an internal (flavour) space. Moreover, these mass terms generally involve opposite effective chiralities, similarly to a Dirac mass term. The net effect of these features is that the Majorana condition does not imply a Majorana mass term. Accordingly the obtained Majorana spinors, as well as the resulting symmetry breaking pattern and low-energy spectrum, are qualitatively different from the ones known in particle physics. This result has important phenomenological consequences, e.g. implies that these mass terms are unsuitable to induce an effective see-saw mechanism, proposed to give mass to neutrinos. Finally, we introduce and discuss schemes based on space-dependent pairings with nonzero total momentum to illustrate how genuine Majorana mass terms may emerge in low-energy quantum systems.

Atomic Quantum Technologies for Quantum Matter and Fundamental Physics Applications

“…Later on, Dirac mass terms have been conceived for Weyl fermions [767] also via the Wilson mechanism (a method to give mass to lattice fermions avoiding ambiguities from different lattice momenta [768]) [769] In the latter approach, a direct effective realization of axion electrodynamics (possibly from a Peccei-Quinn scheme, a proposed method for the solution of the CP problem in the strong sector, exactly based on a similar (pseudo)scalar boson [770]) is obtained [769,771]. Following similar ideas, proposals have been conceived for the Majorana equation [772] (designed for trapped ions platforms) and for Majorana fermions, that means massive fermions with Majorana mass terms [773]. Finally, still concerning relativistic quantum mechanics, we report the theoretical proposal for Nambu-Jona-Lasinio models [774,775]) in [767], and low-dimensional fermionic models, as the Thirring and Gross-Neveu models [776].…”

Exact diagonalization of cubic lattice models in commensurate Abelian magnetic fluxes and translational invariant non-Abelian potentials

“…The possibility of implementing tunable gauge potentials became a paradigmatic example of the tools that can be exploited in the experimental design of novel quantum phases of matter and is providing a remarkable arena of challenging mathematical developments. Such tools prompted a huge variety of theoretical investigations, aimed to propose new realizations of non-trivial phenomena and models, including the study of the physics of the Hofstadter butterfly [5,19,20], Weyl, Dirac and Majorana fermions [21][22][23][24][25], extra dimensions [26][27][28] and the implementation of states with non-Abelian excitations [29]. As an example of application of synthetic gauge potentials, relevant for the purposes of this paper, we observe that in two dimensions one can obtain Dirac cones in square lattices with a magnetic π-flux (half of the elementary flux) threading each plaquette [30][31][32][33].…”