Collective Excitations in a Landau-Majorana Liquid

Landau-Fermi liquid theory is one of the foundational theories of interacting many-body fermions. Its simplicity has led to its continued application to real materials, and the rare instances where it fails (e.g., the case of a non-Fermi liquid) have become a major concern in the condensed matter community. In this study, we apply the formalism of Landau-Fermi liquid theory to describe a quantum liquid of interacting Majorana fermions. As opposed to Majorana zero modes, which characterize topologically non-trivial materials and obey anyonic statistics, Majorana fermions are spin-1/2 particles that experience mutual pairwise annihilation. Drawing on a previous work (arXiv:1709.04483), we describe the quasiparticles in such a system and construct the Landau-Silin kinetic equation. The presence of a robust Fermi surface in the screened Majorana system leads to a Lifshitz transition in the limit of large driving frequency. In addition, a calculation of the zero sound leads to the presence of an enhanced stability of the Landau-Majorana liquid against Pomeranchuk instabilities. These results lead to important differences in the fundamental physics of interacting Majorana fermion ensembles that has potential applications in various condensed matter systems and astrophysical phenomena.