Physics – Condensed Matter – Mesoscale and Nanoscale Physics
Scientific paper
2011-07-08
Solid State Communications 151 (2011) 1894-1898
Physics
Condensed Matter
Mesoscale and Nanoscale Physics
19 pages, 5 figures
Scientific paper
10.1016/j.ssc.2011.09.028
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 tunning the numerical values of the long range interaction. The values of these interactions themselves display a fractal character.
Bhattacharya Nitai
Chakrabarti Arunava
Pal Biplab
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