Fermions with cubic and quartic spectrum

TL;DR

This paper investigates exotic fermions with higher-order momentum spectra near topological Fermi points, analyzing how symmetry violations cause these points to split into multiple Dirac points with linear spectra.

Contribution

It introduces a theoretical framework for understanding fermions with spectra E^2 ~ p^{2N} and describes how symmetry breaking affects their splitting into multiple Dirac points.

Findings

Fermions with spectrum E^2 ~ p^{2N} can emerge near topological Fermi points with charge N.

Breaking symmetry causes these points to split into N Dirac points with linear spectra.

The study provides insights into the topological and spectral properties of exotic fermions.

Abstract

We study exotic fermions with spectrum E^2 ~ p^{2N}. Such spectrum emerges in the vicinity of the Fermi point with multiple topological charge N, if special symmetry is obeyed. When this symmetry is violated, the multiple Fermi point typically splits into N elementary Fermi points -- Dirac points with N=1 and spectrum E^2 ~ p^2 .