One-dimensional potential for image-potential states on grapheme

• Published in: New journal of physics Vol. 16; pp. 1 - 21
• Main Authors: de Andres, P L, Echenique, P M, Niesner, D, Fauster, Th, Rivacoba, A
• Format: Journal Article
• Language: English
• Published: 01.02.2014
• Subjects: Approximation; Binding energy; Dielectrics; Graphene; Mathematical analysis; Mathematical models; Schroedinger equation; Slabs
• ISSN: 1367-2630; 1367-2630
• DOI: 10.1088/1367-2630/16/2/023012

In the framework of dielectric theory, the static non-local self-energy of an electron near an ultra-thin polarizable layer has been calculated and applied to study binding energies of image-potential states near free-standing graphene. The corresponding series of eigenvalues and eigenfunctions have been obtained by numerically solving the one-dimensional Schrodinger equation. The image-potential state wave functions accumulate most of their probability outside the slab. We find that the random phase approximation (RPA) for the non-local dielectric function yields a superior description for the potential inside the slab, but a simple Fermi-Thomas theory can be used to get a reasonable quasi-analytical approximation to the full RPA result that can be computed very economically. Binding energies of the image-potential states follow a pattern close to the Rydberg series for a perfect metal with the addition of intermediate states due to the added symmetry of the potential. The formalism only requires a minimal set of free parameters: the slab width and the electronic density. The theoretical calculations are compared with experimental results for the work function and image-potential states obtained by two-photon photoemission.