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

Electronic fractal patterns in building Sierpinski-triangle molecular systems

“…1, have inspired theoretical studies on fractal Sierpinski triangle samples with different purposes such as exploring spin polarization features 10 and the emergence of flat bands. 11–13 In particular, extended eigenstates are verified in the spectrum of hexagonal ST [Fig. 1(d)], revealed as continuous bands as the lattice is threaded by magnetic fluxes.…”

Tunable caging of excitation in decorated Lieb-ladder geometry with long-range connectivity

“…The method can be applied practically to any quasi-one-dimensional system and has already been employed to study the controlled caging of excitation in different networks. [54][55][56][58][59][60] Starting from a finite generation of scale invariant fractal network, after suitable steps of decimation [55,56] one can produce a Lieb ladder geometry with a diamond plaquette embedded into it (as discussed in the above discussion). The renormalized potential of the top vertex of the diamond is now a complicated function of energy and flux.…”

Application of the real space decimation method in determining intricate electronic phases of matter: a review

“…19,20 Some decorated lattices, described by a tight binding Hamiltonian, possess a typical character due to which one or more bands for a lattice geometry (Fig. 1) may become dispersionless and the corresponding single-particle energy spectrum E(k) becomes independent of momentum k. The so called flat bands [21][22][23][24][26][27][28][29][30][31][32][33][34][35][36] are produced. Such bands arise as a consequence of consecutive destructive interference caused by the geometrical arrangement of the lattice points.…”

“…1) may become dispersionless and the corresponding single-particle energy spectrum E ( k ) becomes independent of momentum k . The so called flat bands 21–24,26–36 are produced. Such bands arise as a consequence of consecutive destructive interference caused by the geometrical arrangement of the lattice points.…”