Fermions with cubic and quartic spectrum

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 .