Engineering flat electronic bands in quasiperiodic and fractal loop geometries

Abstract

Exact construction of one electron eigenstates with flat, non-dispersive bands, and localized over clusters of various sizes is reported for a class of quasi-one dimensional looped networks. Quasiperiodic Fibonacci and Berker fractal geometries are embedded in the arms of the loop threaded by a uniform magnetic flux. We work out an analytical scheme to unravel the localized single particle states pinned at various atomic sites or over clusters of them. The magnetic field is varied to control, in a subtle way, the extent of localization and the location of the flat band states in energy space. In addition to this we show that, an appropriate tuning of the field can lead to a re-entrant behavior of the effective mass of the electron in a band, with a periodic flip in its sign.

9 pages, 8 figures

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• Many-Body Physics with Ultracold Gases
• Edge states in Graphene: from gapped flat band to gapless chiral modes
• Anderson localisation in tight-binding models with flat bands
• Metal-insulator transition in an aperiodic ladder network: an exact result
• Flat band analogues and flux driven extended electronic states in a class of geometrically frustrated fractal networks
• Low-temperature thermodynamics of one class of flat-band models

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