# Universal Signatures of Majorana-like Quasiparticles in Strongly Correlated Landau-Fermi Liquids

## TL;DR

This paper extends Landau-Fermi liquid theory to systems of Majorana-like quasiparticles, revealing unique collective modes and phase transitions, and suggesting new stability features absent in conventional Fermi liquids.

## Contribution

It introduces a Landau-Majorana kinetic equation and demonstrates novel phenomena such as Lifshitz transitions and stable zero sound modes in Majorana-like systems.

## Key findings

- Discovery of Lifshitz transition at specific frequencies.
- Existence of stable zero sound mode in Landau-Majorana liquids.
- Suppression of Pomeranchuk instabilities in certain regimes.

## Abstract

Motivated by recent experiments in the Kitaev honeycomb lattice, Kondo insulators, and the "Luttinger's theorem-violating" Fermi liquid phase of the underdoped cuprates, we extend the theoretical machinery of Landau-Fermi liquid theory to a system of itinerant, interacting Majorana-like particles. Building upon a previously introduced model of "nearly self-conjugate" fermionic polarons, a Landau-Majorana kinetic equation is introduced to describe the collective modes and Fermi surface instabilities in a fluid of particles whose fermionic degrees of freedom obey the Majorana reality condition. At large screening, we show that the Landau-Majorana liquid harbors a Lifshitz transition for specific values of the driving frequency. Moreover, we find the dispersion of the zero sound collective mode in such a system, showing that there exists a specific limit where the Landau-Majorana liquid harbors a stability against Pomeranchuk deformations unseen in the conventional Landau-Fermi liquid. With these results, our work paves the way for possible extensions of the Landau quasiparticle paradigm to nontrivial metallic phases of matter.