Localized states in the continuum in low-dimensional systems

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.

7 pages, 4 figures. To appear in Phys. Rev. B

References in corpus (5)

• Fano Resonances in Electronic Transport through a Single Electron Transistor
• Ab initio analysis of electron-phonon coupling in molecular devices
• Fano resonances and Aharonov-Bohm effects in transport through a square quantum dot molecule
• Scattering theory on graphs (2): the Friedel sum rule
• Connecting wave functions at a three-leg junction of one-dimensional channels

Cited by in corpus (9)

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• Higher-order topological insulators and semimetals in generalized Aubry-André-Harper models
• Floquet bound states in the continuum
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• Chiral bound states in the continuum
• Optical lattices with exceptional points in the continuum
• Non-Hermitian tight-binding network engineering
• Exact dynamics and bound states of a cavity coupled to a two-dimensional reservoir
• Stationary states in a potential well