Surface states in topological semimetal slab geometries

Weyl semimetals are topological materials with protected Weyl nodes in the band structure. In these materials the surface states form open curves at the Fermi surface, Fermi arcs in Weyl semimetals and drumhead states of nodal-line semimetals. In this work we solve analitically the wave function of the surface states in a generic continuous model describing Weyl and nodal-line type I-II semimetals within a slab geometry. Depending on the values of the parameters, different types of Fermi arcs and drumhead states appear. When the mass terms are dominant with respect to the Fermi velocity in the Hamiltonian the decay of the surface states become oscillatory. This property has important consequences in the stability of surface states in a slab geometry This exact solution can be used for a better understanding of the behaviour of Fermi Arcs in real materials and their influence in transport and optical properties. We use these solutions to study the Joint Density of States at the surface which can be used to interpret quasi-particle interference data in scanning tunnneling microscope experiments. We show that oscillatory decay can be distinguish from simple exponential decay of the surface states in these experiments.