FRACTAL FEATURES OF THE QUANTIZED SCANNING TUNNELING CURRENT AND THE LOCAL DENSITY OF STATES FOR A QUANTUM CORRAL

Abstract

We found that quantization of the scanning tunneling microscope (STM) current becomes apparent as the size of a quantum corral (QC) decreases and the corral thickness increases. It is shown that STM current images provide the position dependence of the conduction channels and local density of states (LDOS) images provide the spatial distribution of differential conductance channels. We clarified for the first time that there exist fractal structures in the QC size dependence of the [Formula: see text]–[Formula: see text] characteristic and in that of the LDOS. LDOS images also exhibit a fractal structure as a function of bias voltage. These results demonstrate fractal structures in energy space and real space. For an extremely large QC, we found that the [Formula: see text]–[Formula: see text] curve becomes Ohmic and the LDOS converges to a constant corresponding to the bulk two-dimensional density of states.