Profiles of atomic states as seen by STM

In this section, we study the images of atomic states. Starting with an analytic expression of the tunneling conductivity distribution, we will eompare the theoretical predictions and experimental findings of an easily measurable quantity the radius of the STM image of an atomic state near its peak. 

To determine the image, the first step is to determine the distribution of tunneling current as a function of the position of the apex atom. We set the center of the coordinate system at the nucleus of the sample atom. The tunneling matrix element as a function of the position r of the nucleus of the apex atom can be evaluated by applying the derivative rule to the Slater wavefunctions. The tunneling conductance as a function of r, g(r), is proportional to the square of the tunneling matrix element  

Because the equal-conductance contour is independent of an overall constant, we neglect it for convenience. In Table 6.1, the results for three types of m=Q tip states and three types of m=0 sample states are listed. 

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