Faculty of Materials Science, Graduate School, Saitama Institute of Technology, 1690 Fusaiji, Fukaya-city, Saitama, 369-0293, Japan.
J Phys Condens Matter. 2011 Jan 19;23(2):025303. doi: 10.1088/0953-8984/23/2/025303. Epub 2010 Dec 13.
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.
我们阐明了受限在由双势垒构成的二维量子围栏（QC）中的电子的准稳态。结果表明，对于受限在 QC 中的电子，QC 的哈密顿量不是厄米算符，这导致了复本征能，而虚部的倒数给出了电子的寿命。考虑到受限在矩形 QC 中的电子处于准稳态，我们得到了作为二维位置和偏置电压的显式函数的 STM 图像表达式。从这些表达式中，我们阐明了表面局域态密度（LDOS）、概率密度、形貌图像和微分电导（dI/dV）图像之间的关系。我们首次指出了存在一个滤波函数，它将 dI/dV 图像与 LDOS 图像连接起来。我们的结果再现了在矩形 QC 中观察到的形貌和 dI/dV 模式下的所有实验 STM 图像。此外，我们指定了表征这些 STM 图像的电子态的主要成分。
