Deriving Fermi Arcs of Generic Nature Spanning Nodes Featuring Multibands, Nonlinear Dispersion, and/or Multipoles

Fermi arcs appear as the surface states at the boundary of a three-dimensional topological semimetal with the vacuum, reflecting the Chern number (C) of a nodal point in the momentum space, which represents singularities (in the form of monopoles) of the Berry curvature. They are finite arcs, attaching/reattaching with the bulk-energy states at the tangents of the projections of the Fermi surfaces of the bands meeting at the nodes. The number of Fermi arcs grazing onto the tangents of the outermost projection equals C, revealing the intrinsic topology of the underlying bandstructure, which can be visualised in experiments like ARPES. Here we outline a generic procedure to compute these states for generic nodal points, (1) whose degeneracy might be twofold or multifold; and (2) the associated bands might exhibit isotropic or anisotropic, linear- or nonlinear-in-momentum dispersion. This also allows us to determine whether we should get any Fermi arcs at all for C = 0, when the nodes host ideal dipoles.