Unified Perturbation Theory for STM and SFM

Abstract

In this chapter, we describe perturbation theory for STM and SFM. To understand the influence of tip electronic states and the tip-;sample interactions in the imaging process, and to interpret the observed images, perturbation theory provides a simple and straightforward picture. First, besides STM, there are a number of experimental methods which contribute to the understanding of the sample surface as well as the tip. From an experimental point of view, the perturbation theory can provide insights for the understanding of the images from the properties of the bare tip and the bare sample, thus to achieve a conceptual understanding of the relations among different experimental measurements. Second, first-principles numerical calculations of the electronic structures of the free sample and the free tip have reached a high level of sophistication that a detailed comparison with those experimental measurements has become everday practice. Perturbation theory can bring the results of those calculations together and make predictions to the STM and SFM images. A consistency among the results from different approaches is a sign of true understanding. In words, a natural way of bringing various theoretical and experimental fields into a unified picture is through a proper perturbation theory. Finally, the perturbation theory provides a natural linkage between the tunneling phenomenon and attractive atomic forces through the concept of resonance, which is the foundation of Pauling’s theory of the chemical bond. As we shall see, this brings about a unified perturbation theory of STM and AFM.