Abstract
We provide an exact analytical technique to obtain within a lattice model the wave functions of the edge states in zigzag- and bearded-edge graphene, as well as of the Fermi-arc surface states in Weyl semimetals described by a minimal bulk model. We model the corresponding boundaries as an infinite scalar potential localized on a line, and respectively within a plane. We use the T-matrix formalism to obtain the dispersion and the spatial distribution of the corresponding boundary modes. Furthermore, to demonstrate the power of our approach, we write down the surface Green’s function of the considered Weyl semimetal model, and we calculate the quasiparticle interference patterns originating from an impurity localized at the respective surface.
Highlights
Systems which exhibit edge states, be they topological or not, one, two- or three-dimensional, superconducting or normal, have come under intense scrutiny over the past years
We provide an exact analytical technique to obtain within a lattice model the wave functions of the edge states in zigzag- and bearded-edge graphene, as well as of the Fermi-arc surface states in Weyl semimetals described by a minimal bulk model
We have proposed an analytical route to calculate the boundary modes of graphene and Weyl semimetals within a lattice model
Summary
Systems which exhibit edge states, be they topological or not, one-, two- or three-dimensional, superconducting or normal, have come under intense scrutiny over the past years. The core of the technique consists of modeling the boundary as a point-, line-, or plane-like localized scalar impurity potential with an infinite amplitude This model can be solved exactly using the T-matrix formalism and allows to obtain in a very elegant and straightforward analytical manner the energy dispersion and the wave function of the bound states, as well as the surface/edge Green’s functions of the system.
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