First-Principles Study of Time-Dependent Phenomena in Photon-Assisted Tunneling: I. An Electron Injected into Two-Dimensional Lozenge Quantum Dot

Abstract

We theoretically study the dynamical properties of an electron confined in a two-dimensional (2D) quantum dot (QD) under photon illumination, by solving the time-dependent (TD) Schrödinger equation numerically by the finite difference method in both real space and actual time. To deepen our understanding of the TD features of photon-assisted tunneling (PAT), we employ projection analysis, in which the TD wave function at a QD is decomposed into (static) resonant states by calculating the inner products among them. This analysis further enables the deduction of effective lifetime, by which one can infer the actual period of the electron confined in the QD. The wave number distribution for the transmitted electron is also discussed to examine the propagation of the electron through the system.