Localized states in the continuum in low-dimensional systems

TL;DR

This paper demonstrates that localized states in the continuum can exist in open low-dimensional systems with channeled leads, leading to sharp Fano resonances in transport phenomena.

Contribution

It introduces a new mechanism for localized states in the continuum in low-dimensional open systems, distinct from classical models.

Findings

Localized states can be sustained in low-dimensional open systems.

These states lead to infinitely sharp Fano resonances.

The states have a different origin than traditional continuum states.

Abstract

It is shown in this paper that for open systems, states which are localized in space, discrete in energy, and embedded in the continuum of extended states, can be sustained by low-dimensional and channeled leads. These states have an origin different from that of analogous states discussed by J. von Neumann and E. Wigner [Phys. Z., vol. 30, 465 (1929)]. A few representative systems are discussed. These states cause, for example, infinitely sharp Fano resonance in transport when they are marginally destroyed.