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 response of the system with the modulation of the anisotropy parameter is also studied. Supportive calculation of spectral landscape and demonstration of band dispersion plot are presented to solidify the analytical results. Variation of effective mass tensor cites re-entrant behavior with respect to the modulation of offdiagonal anisotropy. The tunability of those states leads to the controlled decay of wave function envelope. The impact of uniform magnetic perturbation on the bound states has also been discussed. Continuous variation of flux modulates the position of the flat band modes. The macroscopic degeneracy associated with the modes is retained with respect to the application of perturbation.

Linearized spectral decimation in fractals

“…Recent developments with experimental techniques [1][2][3][4] , open possibilities to study condensed matter systems with complex geometry structures like fractals on the atomic level. Theoretical and numerical works on fractals appeared recently include topics such as conductivity and optical properties [5][6][7][8] , localization 9,10 , topology of fractals [11][12][13][14][15] , appearance of flat bands [16][17][18][19] , and others 20,21 .…”

Linearized spectral decimation in fractals

“…Recent developments of experimental techniques [1][2][3][4][5][6] open possibilities to study condensed-matter systems with complex geometries (for example, fractals) at the atomic level. Many theoretical and numerical works on fractals appeared recently including the studies on transport and optical properties [7][8][9][10][11], electronic localization [12][13][14][15], topology of fractals [16][17][18][19][20], appearance of flatbands [21][22][23][24], and others [25][26][27][28].…”