Abstract
In this work we provide a new direct and non-numerical technique to obtain the surface Green's functions for three-dimensional systems. This technique is based on the ideas presented in Phys. Rev. B 100, 081106(R), in which we start with an infinite system and model the boundary using a plane-like 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.
Highlights
Boundaries of certain condensed-matter systems host unique phenomena
In this work we provide a direct and non-numerical technique to obtain the surface Green’s functions for three-dimensional systems
We 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
Summary
Boundaries of certain condensed-matter systems host unique phenomena. For instance, graphene exhibits zeroenergy zigzag-edge modes [1], and topological insulators exhibit conducting edge or surface states [2,3,4]. A method describing the formation of boundary modes was recently introduced [24] This method can be generalized to any dimensions, and in certain situations it can yield fully analytical results, providing a deeper physical insight than numerical techniques. The resulting Green’s function evaluated on the plane neighboring and parallel to the impurity plane becomes the surface Green’s function (see Fig. 1) We apply this technique to calculate the surface Green’s functions for Weyl semimetals described by two different models [27,28]. IV and V we focus on two-dimensional topological insulators described by the Kane-Mele and Chern-insulator models, respectively, and we obtain the corresponding edge modes.
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