A numerical approach to surface Green’s functions via generalized eigenvalue problems

In material physics, surface Green’s functions are needed to analyze the electronic structures of nanoscale junctions. The algorithm for computing the functions consists of three steps. First, a matrix is generated by solving two equations. Then, the eigenvectors of the matrix are computed. Finally, another equation, which is generated by using the eigenvectors, is solved to produce a surface Green’s function. In numerical computations, a perturbation will be added into the matrix at the first step. As a result, by computing the eigenvectors of the perturbed matrix at the second step, a considerable numerical error of the function will emerge at the third step. In this paper, we modify the algorithm in order to successfully compute surface Green’s functions. We replace the first and second steps in the algorithm by an alternative step so that we can compute the eigenvectors of the matrix without computing the matrix. To show the effect of the modification, we report numerical experiments for computing the surface Green’s functions at GdAs surface using a full orbitals tight-binding model.