A theoretical calculation of tunneling spectroscopy of an electron waveguide with or without a scatterer

Abstract

A theoretical study on the tunneling spectroscopy of an electron waveguide recently observed by Eugster and del Alamo is presented. A narrow electron waveguide coupled with another much wider one by a thin barrier between them is taken as a theoretical model for the leaky electron waveguide implemented by Eugster et al., and the transport properties of electrons are studied comprehensively through the wavefunction of the system. The results demonstrate that the conductance for the current tunneling out the barrier oscillates strongly with the width of the narrow electron waveguide, in line with its conductance steps. The theory is in good agreement with the experiments and confirm that the oscillations of the tunneling current can be considered as a spectroscopy of the 1D DOS (one dimensional electron density of states) in the electron waveguide as proposed by Eugster et al. In order to study the effects of scatterers on the transport properties of the leaky electron waveguide, a δ-function is used to simulate the scattering potential The results show that the presence of even a single scatterer located in the waveguide will lead to obvious distortion of the shape of conductance steps, and will greatly influence the oscillations of the tunneling current observed in clean waveguides. However the effects of scatterers located outside the tunneling barrier on either the conductance steps or the oscillations of the tunneling current are negligible.