Electron Coherence in Mesoscopic Structures

Abstract

The recent rapid progress in nanofabrication and experimental techniques made it possible to investigate a variety of meso-- and nano--scale systems, which were unavailable only a few years ago. Examples include fabrication of high-quality quantum wires in semiconductor heterostructures, of nanoscale hybrid superconductor--normal metal structures, and of a variety of novel (and much smaller) quantum dot and q-bit designs. These technological advances have led to formulation of a number of condensed matter theory problems which are equally important for applications and for the fundamental science. The present proposal aims at filling the exposed gaps in knowledge and at facilitating further development of experimental and theoretical physics of nanoscale structures. Specifically, the two PIs address the following issues: (i) The theory of interacting electrons in a quantum wire which accounts adequately for the non-linear dispersion relation of the electrons. The existing approaches rely on models with {\em linearized} electron spectrum, which fall short of addressing a growing list of experimentally relevant phenomena. (ii) Dynamics of hybrid normal--superconducting systems. A reliable treatment of dissipative phenomena in such structures is not developed as of yet, while rapid progress in fabrication makes finding the proper theoretical treatment methods highly desirable. (iii)~The fundamental limits on relaxation times of a superconducting charge q-bit. The latter is one of the most advanced scalable realizations of a quantum computing device. (iv)~The dynamics and relaxation times of a spin of an electron in a small semiconductor quantum dot. Besides the fundamental importance, these structures are also valuable candidates for quantum computing applications.