In this work we provide a direct and non-numerical technique to obtain the surface Green's functions for three-dimensional systems. This technique is based on the ideas presented by V. Kaladzhyan and C. Bena [Phys. Rev. B 100, 081106(R) (2019)], in which we start with an infinite system and model the boundary using a planelike infinite-amplitude potential. Such a configuration can be solved exactly using the T-matrix formalism. We apply our method to calculate the surface Green's function and the corresponding Fermi-arc states for Weyl semimetals. We also apply the technique to systems of lower dimensions, such as Kane-Mele and Chern insulator models, to provide a more efficient and non-numerical method to describe the formation of edge states.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.