Localization, transport, flux induced extended modes and mobility edge in a self-similar corral substrate

TL;DR

This paper explores how magnetic flux influences localization and extended states in a self-similar fractal substrate, revealing flux-induced mobility edges and quantum transport properties.

Contribution

It demonstrates flux-controlled transition between localized and extended states in a fractal lattice, introducing a novel way to engineer quantum states.

Findings

Flux destroys bounded localized modes, creating continuous sub-bands.

Extended states are robust against disorder and anisotropy.

Mobility edges are characterized by multifractal analysis.

Abstract

We address that a single-band tight-binding Hamiltonian defined on a self-similar corral substrate can give rise to a set of non-diffusive localized modes that follow the same hierarchical distribution. As the lattice, the spatial extent of quantum prison containing a cluster of atomic sites is dependent on the generation of fractal structure. Apart from the quantum imprisonment of the excitation, a magnetic flux threading each elementary plaquette is shown to destroy the boundedness and generate an absolutely continuous sub-band populated by resonant eigen functions. Flux induced engineering of quantum states is corroborated through the evaluation of inverse participation ratio and quantum transport. Moreover, the robustness of the extended states has been checked in presence of diagonal disorder and off-diagonal anisotropy. Flux modulated single-particle mobility edge is characterized through mutlifractal analysis. Quantum interference is the essential issue, reported here, that manipulates the kinematics of the excitation and this is manifested by the workout of persistent current.