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

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 eigenfunctions. Flux induced engineering of quantum states is corroborated through the evaluation of inverse participation ratio and quantum transport. The robustness of the extended states has been checked in presence of diagonal disorder and off-diagonal anisotropy. The conducting region is found to be insensitive against minimal parametric modulation. Flux modulated single-particle mobility edge is characterized through multifractal 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.