Correlated Electron Transport in Mesoscopic Structures

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TECHNICAL SUMMARYThis award supports a theoretical investigation of the dynamic response and time evolution of quantum low-dimensional and mesoscopic systems. The research focuses on theory applicable to experiments with quantum wires, superconducting nano-circuits, and quantum dots. The motivation comes from the advances in experimental techniques enabling the dynamic response measurements and from the challenges the evaluation of these responses present for theory. The project has 3 parts:1.) The PI will investigate the dynamic response functions of one-dimensional quantum systems at high momenta. This regime, important for experiments with quantum wires and spin chains, calls for a development of the theory of a nonlinear Luttinger liquid. This work may be a step towards building a universal theory of one-dimensional nonlinear quantum fluids.2.) A new dynamic regime of a quantum superconducting circuit, an inductively shunted Cooper pair box, will be investigated. This includes building a theory of quantum dynamics of charge fluctuations in a chain of small Josephson junctions.3.) The PI will address exciton formation in a semiconductor quantum dot in contact with a bulk conductor. The information about Kondo effect encoded in the optical absorption spectra is complementary to that obtained in dc transport experiments.To carry out this research, the PI will use a variety of techniques, including diagrammatic expansions; Fermi liquid theory; renormalization group theory; the use of exactly solvable one-dimensional models; bosonization technique; and numerical methods.The research provides educational experiences for students and post-doctoral research associates. The work on this project develops understanding of real materials and proficiency in modern methods of condensed matter theory.NON-TECHNICAL SUMMARYThis award supports theoretical research and education to study the electronic properties of special kinds of wires and other structures which are able to confine electrons to one dimension or even to a localized region - effectively zero dimensions. Ordinary wires are three dimensional as far as the electrons they contain are concerned. As electrons are confined to ever smaller distances along two perpendicular directions, the properties of the resulting fluid of electrons change dramatically leading to interesting new phenomena. Motivated by recent experimental advances, the PI will be working in contact with experiment to develop a theory to understand the time dependent properties of these low-dimensional electronic fluids. The PI will also study circuits composed of superconductors which exhibit a cooperative electronic state at sufficiently low temperatures. Superconductivity is a macroscopic state that exhibits the property of coherence that is a hallmark of quantum mechanical states of the world of atoms and molecules. The PI will pursue interesting new phenomena that emerge when superconducting elements are interconnected. This work contributes to the intellectual foundations of quantum computing in which quantum mechanical states are manipulated to carry out logic operations.This project advances understanding of novel systems and materials, such as nano-wires, quantum dots, and carbon nanotubes, which are potential elements of future electronic technology. This project, devoted to understanding the fundamental physical properties that underpin these systems and as such may have a technological impact. This research provides educational experiences for students and post-doctoral research associates. The work on this project develops understanding of real materials and proficiency in modern methods of condensed matter theory.