Quasi-stationary states of an electron confined in a rectangular quantum corral and STMimages

Abstract

We elucidated quasi-stationary states of an electron confined in a two-dimensional quantumcorral (QC) built up with double barriers having a finite width. It is shown that theHamiltonian of the QC is not a Hermitian operator for an electron confined in the QC,which results in a complex eigenenergy and the inverse of the imaginary part yields thelifetime of the electron. Considering that the electron confined in a rectangular QCstays in a quasi-stationary state, we obtained expressions for STM images as anexplicit function of both the two-dimensional position and the bias voltage. Fromthose expressions, we clarified relations among the surface local density of states(LDOS), the probability density, topographical images and differential conductance (dI/dV) images. We pointed out the existence of a filtering function that connects thedI/dV image with the LDOS image for the first time. Our results reproducedall experimental STM images observed in topographical anddI/dV modes for a rectangular QC. Moreover, we specified the main components of electron statesthat characterize those STM images.