Daniel Gosálbez-Martínez
Institute of Physics, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
National Centre for Computational Design and Discovery of Novel Materials MARVEL, École Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
Weyl nodes with chiral charge +/-1 are classified as types I and type II according to the tilting of
the conical band dispersion at the band degeneracy. Their Fermi surface, described by a quadratic
form, is different for these two types. We extend this classifcation to the case of composite Weyl
nodes with chiral charge larger than one. When the C4 and C6 rotation symmetries forbid the linear
band dispersion on the plane perpendicular to the symmetry axis, new terms with quadratic and
cubic momentum dependence must be included. Consequently, the Fermi surface produced by these
band degeneracies are described by a 4 or 6 order algebraic surfaces. In this more complex situation,
instead of classifying Fermi surfaces, we study numerically the possible Lifshitz transitions of the
Fermi surface produced by a composite Weyl node as the chemical potential is varied. We use this
methodology to classify the different types the composite Weyl fermions. In particular, for the case
of quadratic Weyl nodes generated by the C4 rotation symmetry. we find four different types band
dispersion morphologies, two analogous to the type-I and type-II case of the conical Weyl nodes,
and two new distinct morphologies within the type-II class. We illustrate the existence of these new
types of band degeneracies in real materials such as ferromagnetic iron.