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

TL;DR

This paper constructs a class of fractal networks that host flat-band states and shows how magnetic fields can delocalize these states, revealing new insights into electronic localization in complex geometries.

Contribution

It introduces a method to analytically derive flat-band states in fractal networks and demonstrates magnetic field-induced delocalization effects.

Findings

Existence of infinitely many flat-band states in fractal networks.

Magnetic fields can delocalize localized states, creating continuous energy bands.

Localization can be tuned by electron energy and magnetic flux.

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.