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

TL;DR

This paper investigates the electronic spectrum and magneto-transport properties of a fractal Sierpinski gasket network with embedded Aharonov-Bohm interferometers, revealing exotic electron states and tunable magnetic flux effects.

Contribution

It introduces a novel fractal network model with embedded interferometers, demonstrating exact analytical results on localized and extended states and flux-controlled transport.

Findings

Existence of extreme localized states at specific energies

Presence of staggered localization with delayed spatial localization

Magneto-transport can be precisely tuned by magnetic flux

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.