Impurity-directed Transport within a Finite Disordered Lattice

TL;DR

This paper demonstrates how tuning an impurity's energy in a disordered 1D quantum lattice enables controlled electron transport and oscillations between localized states, despite Anderson localization effects.

Contribution

It introduces a method to control electron transport in disordered lattices by adjusting impurity energy, revealing quasi-periodic oscillations and potential routing mechanisms.

Findings

Electron can oscillate between impurity and localized lattice regions.

Impurity energy tuning induces quasi-periodic electron motion.

Electron transport can be selectively directed across the lattice.

Abstract

We consider a finite, disordered 1D quantum lattice with a side-attached impurity. We study theoretically the transport of a single electron from the impurity into the lattice, at zero temperature. The transport is dominated by Anderson localization and, in general, the electron motion has a random character due to the lattice disorder. However, we show that by adjusting the impurity energy the electron can attain quasi-periodic motions, oscillating between the impurity and a small region of the lattice. This region corresponds to the center of a localized state in the lattice with an energy matched by that of the impurity. By precisely tuning the impurity energy, the electron can be set to oscillate between the impurity and a region far from the impurity, even distances larger than the Anderson localization length. The electron oscillations result from the interference of hybridized states, which have some resemblance to Pendry's necklace states [J. B. Pendry, J. Phys. C: Solid State Phys. 20, 733-742 (1987)]. The dependence of the electron motion on the impurity energy gives a potential mechanism for selectively routing an electron towards different regions of a 1D disordered lattice.