On localization and de localization of electronic states in a class of low dimensional systems

Abstract

n this dissertation we have discussed the central idea of localization and de- newlinelocalization containing the evaluation of the spectral properties of various low- newlinedimensional model systems. We have mainly focused those networks which do not newlinebear any translational invariance. Analytical discussion about the strange kind of newlinelocalization behavior coming out due to the topological nature of the system con- newlinecerned is mentioned in details along with the elaborate calculation of transmission newlineprofile. All such systems we have studied within the tight-binding approximation newlinein respect of their electronic properties, exhibit exotic spectral features. The in- newlineteresting point about this study is that sometimes those spectral landscape can be newlinetuned or perturbed at will by means of some external perturbation or by some def- newlineinite correlations between the parameters of the Hamiltonian of the system. These newlinestrange facts are discussed in the present thesis along with the supportive calcula- newlinetions. The interesting fact is that in all these kind of aperiodic systems there is no newlinetranslational invariance present in the long-range fluctuation. Still it induces certain newlinecritical signature in the nature of the single particle electronic eigenstates, that nor- newlinemally are not apparent in the case of periodic systems. All the supportive analytical newlinecalculations and the results are obtained by computing the local density of states newlineprofile and the energy eigenvalue spectrum of the entire system using the real space newlinerenormalization group method and Greens function approach. The transmission newlinecalculations are also done in some relevant cases using the decimation procedure. newlineHere an important point to be noted that the structures which we have taken, have newlineno long-range periodicity or translational invariance. newline