Conductance of a Quantum Point Contact in the presence of a Scanning   Probe Microscope Tip
  Using the recursive Green's function technique, we study the coherent electron conductance of a quantum point contact in the presence of a scanning probe microscope tip. Images of the coherent fringe inside a quantum point contact for different widths are obtained. It is found that the conductance of a specific channel is reduced while other channels are not affected as long as the tip is located at the positions correspending to that channel. Moreover, the coherent fringe is smoothed out by increasing the temperature or the voltage across the device. Our results are consistent with the experiments reported by Topinka et al.[Science 289, 2323 (2000)]. 
Guang-Ping He, Shi-Liang Zhu, and Z.D. Wang