Electronic states and charge transport in a class of low dimensional structured systems

• Published in: Physica. E, Low-dimensional systems & nanostructures Vol. 114; p. 113616
• Main Author: Chakrabarti, Arunava
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01-10-2019
• Subjects: Decorated lattices single particle states charge transport; Decorated lattices single particle states charge transport
• ISSN: 1386-9477
• DOI: 10.1016/j.physe.2019.113616

This review is an explorer's walk that revisits the character of single particle states and charge transport in a class of low dimensional decorated lattices. The systems considered here possess some kind of structure that are mainly geometric or topological in character. With a brief introduction to the basics wherever necessary, we glance over certain spectral peculiarities observed in a group of crystalline, disordered and hierarchical lattices. We review how local positional correlations or even a minimal quasi-one dimensionality, introduced in an apparently simple way, can bring in non-trivial changes in the energy spectrum and in the transport characteristics of such systems. The discussion is mostly confined to the simplified canvas of non-interacting, spinless electrons described by tight binding models. The effect of interaction between the electrons is only mentioned in the context of transport in one or two cases. The charge transport is mainly discussed in terms of the end-to-end transmission coefficient or the Landauer conductance for open systems, and in terms of the persistent currents in certain closed loop geometries. For an appreciation of the survey, the Green's function formalism and a few the elementary ideas of the real space renormalization group methods are briefly sketched in this article.