On the extendedness of eigenstates in a hierarchical lattice: A critical view

Biplab Pal*, Arunava Chakrabarti, Nitai Bhattacharya

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


We take a critical view at the basic definition of extended single particle states in a non-translationally invariant system. For this, we present the case of a hierarchical lattice and incorporate long range interactions that are also distributed in a hierarchical fashion. We show that it is possible to explicitly construct eigenstates with constant amplitudes (normalized to unity) at every lattice point for special values of the electron-energy. However, the end-to-end transmission, corresponding to the above energy of the electron in such a hierarchical system depends strongly on a special correlation between the numerical values of the parameters of the Hamiltonian. Keeping the energy and the distribution of the amplitudes invariant, one can transform the lattice from conducting to insulating simply by tuning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character

Original languageEnglish
Pages (from-to)1894-1898
Number of pages5
JournalSolid State Communications
Issue number24
StatePublished - Dec 2011
Externally publishedYes


  • A. Hierarchical lattices
  • C. Tight binding Hamiltonian
  • D. Localization


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