High-frequency blockade in a tight-binding one-dimensional lattice with single vibrating atomic state

TL;DR

This paper investigates how a single vibrating atomic site in a one-dimensional tight-binding lattice can cause complete elastic reflection of electrons, revealing high-frequency blockade states with potential applications in quantum dot systems.

Contribution

It introduces the concept of high-frequency blockade states in a 1D lattice with a vibrating site, combining numerical and analytical methods to analyze electron reflection phenomena.

Findings

Identification of conditions for elastic electron reflection (blockade states)

Comparison with free-electron models with vibrating delta potentials

Analysis of local and reflectionless states in the system

Abstract

One-dimensional tight-binding lattice, single site of which possesses harmonically vibrating level is studied. The states of non-interacting electrons incident with fixed energy from infinity are considered. It is shown that at definite conditions the site reflects electrons {\it absolutely and elastically} (high-frequency blockade states). The problem is treated both numerically and (in the case of narrow band) analytically. The results are compared with the free-electron 1D problem with vibrating $\delta$-functional potential. Together with the blockade states the local and reflectionless states are examined. Possible realization of the system as a lattice of quantum dots is discussed.