Electron-scattering-induced entanglement between two atoms placed near the zigzag edge of a phosphorene ribbon

Abstract

In the present work, the scattering of the edge-state electrons from two similar two-level atoms located as impurities near the two sites on the zigzag edge of a phosphorene ribbon has been studied theoretically with a focus on the production of entanglement between the impurities. To this end, it is assumed that the electrons are traveling parallel to the zigzag edge of a phosphorene ribbon and the edge states have been used to describe the state of these mobile electrons. Also, it is presumed that the incident electrons interact with the electric dipole of the scatterer atoms. Then, the general scattering theory based on the Lippmann–Schwinger equation has been applied along with the Green function approach to calculate the transition matrix elements and consequently the transmission and reflection probabilities of the mobile electrons. It has been shown that the problem can be reduced to the scattering of electrons along a one-dimensional chain lying along the zigzag edge of the ribbon. We then show that the scattering process leads to creation of a quantum correlation between the similar atomic impurities. Concurrence has been calculated as a measure of the produced entanglement, and its dependence on the energy of the electrons as well as the interaction strengths has been investigated and discussed. © 2022, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.