Calculation of axial charge spreading in carbon nanotubes and nanotube Y junctions during STM measurement

Distribution of the probability current and the probability density of wave packets was calculated for nanotubes and nanotube Y junctions by solving the three dimensional time-dependent Schrödinger equation for a jellium potential model of the scanning tunneling microscope (STM) tip-nanotube-support system. Four systems were investigated: an infinite single wall nanotube (SWNT) as reference case, a capped SWNT protruding a step of the support surface, a quantum dot (finite tube without support), and a SWNT Y junction. It is found that the spatial distribution of the probability current flowing into the sample is decided by the electron probability density of the tube and by the oscillation in time of the probability current, which in turn is governed by the quasibound states on the tube. For the infinite tube the width of the axial spreading of the wave packet during tunneling is about 5nm. When the STM tip is above that part of the tube which protrudes from the atomic scale step of the support surface it is found that the current flows ballistically along the tube and the total transmission is the same as for the infinite tube. In the case of quantum dot, however, the finite tube is first charged in a short time then it is discharged very slowly through the tip-nanotube tunnel junction. In the Y junction both the above the junction and off the junction tip positions were investigated. For a 1.2nm displacement of the tip from the junction the wave packet still “samples” the junction point which means that in STM and scanning tunneling spectroscopy experiments the signature of the junction should be still present for such tip displacement. For all tunneling situations analyzed the tunnel current is mainly determined by the tip-nanotube junction owing to its large resistance. The tunneling event through the STM model is characterized by two time scales, the nanotube is quickly “charged” with the wave packet coming from the tip then this “charge” flows into the support 50 times slower.