Exotic electron states and tunable magneto-transport in a fractal Aharonov-Bohm interferometer

Abstract

A Sierpinski gasket fractal network model is studied in respect of its electronic spectrum and magneto-transport when each arm of the gasket is replaced by a diamond shaped Aharonov-Bohm interferometer, threaded by a uniform magnetic flux. Within the framework of a tight binding model for non-interacting, spinless electrons and a real space renormalization group method we unravel a class of extended and localized electronic states. In particular, we demonstrate the existence of extreme localization of electronic states at a special finite set of energy eigenvalues, and an infinite set of energy eigenvalues where the localization gets delayed in space (staggered localization). These eigenstates exhibit a multitude of localization areas. The two terminal transmission coefficient and its dependence on the magnetic flux threading each basic Aharonov-Bohm interferometer is studied in details. Sharp switch on- switch off effects that can be tuned by controlling the flux from outside, are discussed. Our results are analytically exact.

arXiv comment8 pages, 8 figures

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Cited by in corpus (3)

• Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks
• Effects of heterogeneity in site-site couplings for tight-binding models on scale-invariant structures
• Flux-induced strengthening of the magnetic couplings in a flat-band diamond chain