TY - JOUR
T1 - On the extendedness of eigenstates in a hierarchical lattice
T2 - A critical view
AU - Pal, Biplab
AU - Chakrabarti, Arunava
AU - Bhattacharya, Nitai
N1 - Funding Information:
One of the authors (B. Pal) acknowledges financial assistance from DST , India through the INSPIRE fellowship.
PY - 2011/12
Y1 - 2011/12
N2 - 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
AB - 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
KW - A. Hierarchical lattices
KW - C. Tight binding Hamiltonian
KW - D. Localization
UR - http://www.scopus.com/inward/record.url?scp=80655136998&partnerID=8YFLogxK
U2 - 10.1016/j.ssc.2011.09.028
DO - 10.1016/j.ssc.2011.09.028
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AN - SCOPUS:80655136998
SN - 0038-1098
VL - 151
SP - 1894
EP - 1898
JO - Solid State Communications
JF - Solid State Communications
IS - 24
ER -