Type-II quadratic and cubic Weyl fermions

Abstract

Type-II Weyl fermions characterized by tilted energy dispersions have attracted significant interest because such quasiparticles exhibit unique properties due to their open Fermi surfaces. Herein, we propose type-II quadratic (cubic) Weyl fermions by combining tilted energy dispersions with higher Chern numbers $\mathcal{C}=\ifmmode\pm\else\textpm\fi{}2$ ($\ifmmode\pm\else\textpm\fi{}3$), making the classification of chiral fermions more complete. Unlike type-II Weyl fermions with tilted energy dispersions along any direction, type-II quadratic (cubic) Weyl fermions can only be tilted along a rotational axis. Our analytical solutions of Landau levels and magneto-optical spectra show that type-II quadratic (cubic) Weyl fermions have unique absorption properties, such as different locations and widths of the absorption peaks compared with known chiral fermions, which can be used as a reference to detect these Weyl fermions in experiments. Using first-principles calculations, we identify the type-II quadratic Weyl fermions in cubic ${\mathrm{CaGe}}_{2}$, in which the electron and hole pockets touch at the nodes with $\mathcal{C}=+2$ and two visible Fermi arcs come out from the type-II quadratic Weyl points.