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

We elucidated quasi-stationary states of an electron confined in a two-dimensional quantum corral (QC) built up with double barriers having a finite width. It is shown that the Hamiltonian 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 the lifetime of the electron. Considering that the electron confined in a rectangular QC stays in a quasi-stationary state, we obtained expressions for STM images as an explicit function of both the two-dimensional position and the bias voltage. From those 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 the dI/dV image with the LDOS image for the first time. Our results reproduced all experimental STM images observed in topographical and dI/dV modes for a rectangular QC. Moreover, we specified the main components of electron states that characterize those STM images.