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.

已报告了分层3单复形分形几何的非色散平带模式的显式构造及其可调谐性。为确定性自相似非平移不变网络定义的单带紧束缚哈密顿量可以产生这种自定位本征态的无穷大，为此波包被困在原子位点的特征簇内。详细说明了检测那些无色散状态的分析处方。这些状态被局限在大小不断增加的集群上，这表明存在大量的局域化区域。本地化的发作可以在原则上，在空间“延时”由电子的能量的适当选择。这些状态的可调性导致波动函数包络的受控衰减。还讨论了摄动对束缚态的影响。还讨论了类似的波导模型。