Surface states and finite size effects in triple-fold semimetals

Triple-fold or pseudospin-1 semimetals belong to a class of multi-fold materials in which linearly dispersive bands and flat bands intersect at the same point, forming triple-fold crossing points. We conduct an analytical investigation of topologically protected Fermi arc surface states and finite-size effects in three-dimensional (3D) triple-fold and doubly degenerate triple-fold semimetals in continuum low-energy models. Higher topological charge of the triple-fold crossing points leads to two Fermi arcs connecting the nodes. For a single triple-fold crossing point, we found that no term in the Hamiltonian with momentum-independent elements can open a gap, prompting us to consider a doubly-degenerate triple-fold fermion, where the gap can be opened by mixing the degenerate copies. Thin films of triple-fold semimetals allow for mixing between the surface and bulk states in addition to the discretization of energy levels of the latter.