Controlled imprisonment of wave packet and flat bands in a fractal geometry

Abstract The explicit construction of non-dispersive flat band modes and the tunability has been reported for a hierarchical 3-simplex fractal geometry. A single tight-binding Hamiltonian defined deterministic self-similar non-translationally invariant network can give rise to countably infinity such self localized eigenstates which wave packet gets trapped inside characteristic cluster atomic sites. An analytical prescription detect those dispersionless states demonstrated elaborately. are over clusters increasing sizes, displaying existence multitude localization areas. onset can, in principle, be ‘delayed’ space by an appropriate choice energy electron. leads controlled decay function envelope. impact perturbation on bound also discussed. analogous guide model