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We have investigated the Scanning Tunneling Microscopy (STM) of graphite with varying tip-to-surface distance. Using an LCAO type approach we showed that at small separations states are localized between the tip and the surface. The energies and the characters of these Tip Induced Localized States (TILS) depend on the height and the lateral position of the tip. These states play a significant role in the tunneling process and influence the STM corrugations predicted from the local density of states. We have developed a current expression, which includes these local interactions, but differes significantly from earlier theories.
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Tekman et al. (1988) studied this question.
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