Novel Ordered States of Electrons

University Of California-Los Angeles, Los Angeles CA

Investigators

Abstract

This award supports theoretical research that is devoted to some of the rich and complex states of matter in which electrons can organize themselves in solids. The intellectual merits of the work drive from its main goals: a characterization of the universal properties of these states; an elucidation of their experimental signatures; and a determination of the particular materials in which, and the conditions under which, they can occur. This work will focus on three primary classes of states. (1) Ordered states of the interacting electron gas in the presence of impurities. The goal is a better understanding of the phase diagrams of electrons in two- and three-dimensions as a function of disorder strength and inter-electron spacing. One particularly fascinating possibility is that random impurities may actually facilitate the development of electronic ordering. (2) Density-wave states of non-zero angular momentum. The goal is to elucidate their interplay with superconductivity and magnetism, and their possible role as 'hidden' orders which lead to puzzling behavior in correlated electron materials. Considerable experimental and theoretical interest is focused on determining whether d-density wave order occurs in the cuprate superconductors. (3) Non-Abelian topological states of quantum magnets, quantum dot arrays, and Josephson junction arrays. If a system with non-Abelian braiding statistics were realized in nature, it would be an attractive arena for quantum computation because the richness of this type of braiding statistics permits universal computation through braiding operations and because the quantum information is encoded in topological relations which are automatically protected against the local effects of decoherence. However, very little is known about the conditions under which such states occur. The principle aim of this project is to shed light on this question. The research will be integrated with teaching and training. The PI also plans to complete a textbook on quantum condensed matter theory from a modern perspective. %%% This award supports theoretical research that is devoted to some of the rich and complex states of matter in which electrons can organize themselves in solids. The intellectual merits of the work drive from its main goals: a characterization of the universal properties of these states; an elucidation of their experimental signatures; and a determination of the particular materials in which, and the conditions under which, they can occur. The research will be integrated with teaching and training. The PI also plans to complete a textbook on quantum condensed matter theory from a modern perspective. ***