Engineering flat electronic bands in quasiperiodic and fractal loop geometries

TL;DR

This paper presents an analytical method to engineer flat electronic bands and control electron localization in quasiperiodic and fractal loop geometries using magnetic flux, revealing tunable localization and re-entrant effective mass behavior.

Contribution

It introduces a novel analytical scheme to construct and manipulate flat bands and localized states in complex looped networks with quasiperiodic and fractal structures.

Findings

Controlled localization of electronic states via magnetic flux.

Re-entrant behavior of effective mass with magnetic tuning.

Analytical construction of flat bands in complex 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.