Analytical Formulae for the Surface Green’s Functions of Graphene and 1T’ MoS2 Nanoribbons

Abstract

Surface Green’s functions describe the coupling of the device region with the attached leads. A lead represents a semi-infinite region with uniform properties such as cross section and electrostatic potential. The scattering states in the leads can be determined in different ways. In this work we exploit the uniformity of the system and formulate the problem in reciprocal space where the Green’s function takes on a simple form. A Fourier transformation yields the elements of the Green’s function in real space. We present the principal steps of this calculation and discuss results for nanoribbons. The 2D materials considered are graphene and $\mathrm{M}\mathrm{o}\mathrm{S}_{2}$ in the 1T’ phase, their electronic structure is represented by k$\cdot$ p Hamiltonians.