Linearized Quantum Conductivity of Atomic Clusters and Artificial Molecules
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Linearized Quantum Conductivity of Atomic Clusters And Artificial Molecules Liudmila A. Pozhar Western Kentucky University, Department of Chemistry, Bowling Green, KY 42101, U.S.A. ABSTRACT The explicit expression for the linearized longitudinal quantum conductivity of inhomogeneous systems (such as semiconductor atomic clusters, artificial molecules, etc.) in weak electro-magnetic fields derived recently within a first principle quantum statistical mechanical approach in terms of the equilibrium two-time temperature Green functions (TTGFs) has been analyzed to develop analytical and computational means for its calculations. This has been done using a generalized continuous fraction method due to Zubarev and Tserkovnikov (ZT). The TTGFs have been related to Kubo’s relaxation functions of the charge density and its gradients that can be computed using available quantum statistical mechanical algorithms and software. Thus, it becomes possible to predict the linearized quantum conductivity of any small system (in particular small semiconductor quantum dots (QDs)) as a function of external electromagnetic fields using a unified fundamental approach. This knowledge can be used to develop small semiconductor QD-based highly sensitive tunable sensors based on changes in the conductivity caused by external electromagnetic fields (in particular, radiation). INTRODUCTION Virtual (or fundamental theory-based, computational) synthesis of novel nanomaterials, such as small QD-based nanoheterostructures with characteristic unit dimensions in the range of a few nanometers, is an important theoretical tool that allows to elucidate and utilize quantum effectdriven (and in particular, quantum confinement-driven) contributions to the equilibrium and charge transport properties of small systems caused by strong inhomogeneity of these systems. Existing theoretical approaches to charge transport in such systems use fundamental quantum theoretical and computational methods developed for bulk systems [1], and/or of half-heuristic considerations developed for mesoscopic systems that accommodate available experimental evidence through adjustable parameters and approximate evaluations [2]. Correspondingly, the theoretical results so obtained can not be used for accurate predictions of the electronic transport properties of sub-nanostructured materials or atomic/molecular clusters composed of a few tenths of atoms, or artificial molecules. Moreover, such methods have to be dramatically modified for every nanosystem and with every emerging experimental evidence. This makes extremely difficult the development of unified theoretical/computational methods applicable to large classes of such systems. Recently, a novel approach [3] that originates in quantum statistical mechanics and quantum field theory was developed to express the charge transport properties and susceptibilities of the small quantum systems in terms of the equilibrium TTGFs. The local charge and current conservation equations and explicit analytical expressions for
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