Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks

Abstract

We demonstrate, by explicit construction, that a single band tight binding Hamiltonian defined on a class of deterministic fractals of the b = 3N Sierpinski type can give rise to an infinity of dispersionless, flat-band like states which can be worked out analytically using the scale invariance of the underlying lattice. The states are localized over clusters of increasing sizes, displaying the existence of a multitude of localization areas. The onset of localization can, in principle, be delayed in space by an appropriate choice of the energy of the electron. A uniform magnetic field threading the elementary plaquettes of the network is shown to destroy this staggered localization and generate absolutely continuous sub-bands in the energy spectrum of these non-translationally invariant networks.

9 pages, 9 figures, 1 Table

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• Electronic properties and quantum transports in functionalized graphene Sierpinski carpet fractals
• Flux modulated flat band engineering in square-kagome ladder network
• Linearized spectral decimation in fractals
• Aharonov-Bohm caging of an electron in a quantum fractal
• A fractal geometry immersed in a hierarchical magnetic flux distribution
• Topological Degeneracy Induced Flat Bands in two-Dimensional Holed Systems