Disorder and interaction in topological matter

Brown University, Providence RI

Investigators

Abstract

NONTECHNICAL SUMMARY This award supports research and education on the theory of topological quantum materials. Progress on electronic device miniaturization has culminated in the ability of modern technology to confine electrons at the nanoscale. Such confinement results in drastically changed material properties. A striking example is the fractional quantum Hall effect, where electrons behave as if they were split into several smaller particles, called anyons. The properties of anyons are unlike those of any other particles in nature, and can be used for potential applications in topological quantum computing, which is uniquely free of errors that are inherent in all other approaches to quantum computing. As a consequence, a topological quantum computer could accomplish the same tasks as a much larger non-topological quantum computer but with fewer qubits. The project aims at understanding the properties of anyons, which is a critical open problem. The PI will collaborate closely with experimental groups, and incorporate research insights from the field of topological insulators. Topological insulators are new materials that do not conduct electricity in the bulk like their conventional relatives rubber and plastic. However, in contrast to rubber and plastic, their surface forms a conductor. The PI will investigate the flow of electric current on the surfaces of topological insulators in the presence of material disorder. In addition to research, the award supports several educational and outreach activities. Most of the budget will be directed towards supporting graduate students. Other activities will involve advising undergraduate students, performing outreach at different school grade levels, and organizing a scientific conference. Graduate and undergraduate research on novel materials will contribute to the scientific education of the US workforce. TECHNICAL SUMMARY This award supports research and education on the theory of topological quantum materials. The properties of topological materials are dramatically different from others, particularly in the presence of strong interactions, or quenched disorder. For example, Coulomb interaction leads to the formation of fractional quantum Hall states, where electrons fractionalize into anyons, a theoretical prediction that opens up possibilities of great importance for basic research and applications, and that has stimulated much experimental work. The first thrust of this project is motivated in part by recent experiments and focuses on the nature of the fractional quantum Hall states in the second Landau level in GaAs systems. The other motivation of the first thrust comes from the recent breakthrough work that connected theoretical ideas about surface states of topological insulators with 2D electron gases at half-filling. The project explores related physics in the absence of particle-hole symmetry at filling factor 5/2, and uses it to explain experimental data. The research addresses the effect of strong interactions on the existing experimental tools, and in collaboration with experimentalists' aims at developing new approaches to probing anyons. Topological properties are robust with respect to weak quenched disorder, but strong disorder may lead to striking effects, such as the formation of a metallic phase in 3D topological insulators. The second thrust of the project investigates the physics of that unusual metal. The project explores the crossover between bulk and surface disorder by considering insulators with fractal surfaces, as well as transport in low-dimensional structures based on topological insulators. In addition to research, the award supports several educational and outreach activities. Most of the budget will be directed towards supporting graduate students. Other activities will involve advising undergraduate students, performing outreach at different school grade levels, and organizing a scientific conference. Graduate and undergraduate research on novel materials will contribute to the scientific education of the US workforce.