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 corresponding 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 [Science 289, 2323 (2000)].