Local modification of sample wavefunction

First-principles calculations of an STM, including a real tip and a real sample, clearly show that within the normal tip-sample distances (3.-6 A from nucleus to nucleus), in the gap region, the local electronic density resembles neither that of the tip nor that of the sample. Substantial local modifications are induced by the strong interaction. An example is the system of an A1 sample with an A1 tip, calculated by Ciraci, Baratoff, and Batra (1990a), as shown in Fig. 8.1. As the tip-sample distance is reduced to 8 bohr, the electron density begins to show a substantial concentration in the middle of the gap. This phenomenon becomes much more pronounced when the tip-sample distance is reduced to about 7 bohr. These distances are exactly the normal distances where atom-resolved images are obtained. 

The modification of an x-wave sample state due to the existence of the tip is similar to the case of the hydrogen molecule ion. For nearly free-electron metals, the surface electron density can be considered as the superposition of the x-wave electron densities of individual atoms. In the presence of an exotic atom, the tip, the electron density of each atom is multiplied by a numerical constant, 4/e 1.472. Therefore, the total density of the valence electron of the metal surface in the gap is multiplied by the same constant, 1.472. Consequently, the corrugation amplitude remains unchanged. 

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The local modification of sample wavefunctions due to the proximity of the tip, and consequently the involvement of the Bloch functions outside the energy window Er eV in the tunneling process, has an effect on the limit of the energy resolution of scanning tunneling spectroscopy. This effect is discussed in detail by Ivanchenko and Riseborough (1991). First, if the tunneling current is determined by the bare wavefunctions of the sample and the tip, the process is linear, and there is no effect of quantum uncertainty. The effect of quantum uncertainty is due to the modification or distortion of the sample wavefunction due to the existence of the tip. Here, we present a simple treatment of this problem in terms of the MBA. 

Local density of states (continued) definition 119 s-wave-tip model, and 29 Sommerfeld metal 93 STM corrugation, and 142 total charge density, and 120 Local modification of sample wavefunctions 195 Local-density approximation 114 Logarithmic amplifier 257 Louse 269... 

Tip-sample interactions 36, 195—210 force and deformation 37 local modification of sample wavefunctions 195 uncertainty principle, and 197 wavefunction modification 37 Topografiner 44—47 Topographic images 122, 125 Transient response 261, 262 Transition probability 67 Transmission electron microscopy 43... 

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