Spectral properties and quantum transport in certain aperiodic lattices in one dimension and beyond

Abstract

The central theme of this Ph.D. dissertation is to highlight the localization newlineand delocalization of single particle states in certain newlinelow dimensional aperiodic lattices, studied within the tight-binding newlineframework. In this thesis, we have also tried to unravel the relevance newlineof this localization and delocalization issue within the current newlinepanorama of Physics. The systems considered here are aperiodic in newlinecharacter with a lack of translational invariance, which exhibit features newlinethat are usually absent in periodic systems. We analyze the newlinespectral character of the electronic states in such systems by evaluating newlinethe density of states (DOS) and the energy eigenvalue spectrum newlineusing the mathematical tools such as real space renormalization newlinescheme (RSRG) and the Green s function method. This thesis newlinereports some exotic behaviors regarding localization and delocalization newlineof single particle electronic eigenstates in certain quasiperiodic newlinelattices and deterministically disordered systems. The results are related newlineto the spectral peculiarities in such systems, and are mostly analytic newlineand exact. The signatures of the electronic states, as obtained newlinefrom the spectral character, are corroborated by the calculation of newlinetwo-terminal transmission coefficient of finite sized systems sandwiched newlinebetween two ideal semi-infinite leads. For this latter part, newlinewe employ a transfer matrix method (TMM) and a real space decimation newlineprocedure, to be described at appropriate places. A major newlineportion of the thesis addresses the possibility of a controlled creation newlineof absolutely continuous bands populated by extended eigenstates newlinein a family of decorated lattices where the building blocks newlineare arranged following quasiperiodic or random fashion. This is unconventional, newlineand thus interesting. Such absolute continuity in the newlineenergy spectrum, is shown to be tunable either by some external newlineperturbation, or by definite numerical correlations between the parameters newlineof the tight-binding Hamiltonian describing the model system.