CAREER: Topological Strings in Three Dimensions

University Of Virginia Main Campus, Charlottesville VA

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education in the development of topological phases of quantum electronic matter in three spatial dimensions. Gas, liquids and solids are classical phases of matter that are distinguished by their collective thermodynamic properties. Similarly, insulators, metals, semiconductors, and superconductors are conventional electronic phases of matter that are distinguished by their electrical characteristics. The recently discovered topological quantum phases are phases of matter in which the underlying system behaves as if it comprises particles possessing fractions of the characteristic properties of its true constituents, e.g. a fraction of the electron charge, a feat impossible in conventional systems. For example, the fractional quantum Hall states are known topological phases in two dimensions that host fractionally charged particles. The PI will investigate the theoretical relationship between topological phases of matter and topological strings in three dimensions. Topological strings are almost one-dimensional objects that emerge under certain conditions; for example, the vortex string created by a whirlpool in a three-dimensional fluid. When realized in a topological phase, topological strings can exhibit technologically desirable characteristics, such as dissipationless transport, i.e. conduction with no loss of energy, and mutually independent transport of energy, spin, and charge. These unconventional electronic transport properties are unique to topological strings in topological phases, and are otherwise impossible to achieve in conventional materials. This research project has significant potential impact not only on the condensed matter community, but also on materials science and engineering, on high-energy physics, and even on pure mathematics. It has the potential to open new frontiers in the theory of electronic matter, and in the realization of new topological materials and technological applications such as a quantum computer. This award also supports broader educational activities: The PI will continue mentoring and training graduate students, including members of underrepresented groups, in advanced theoretical methods. In addition, he will participate in outreach efforts targeting local high schools, and will help connect the general public with scientific research through public talks and physics demonstrations. TECHNICAL SUMMARY This CAREER award supports theoretical research and education in the understanding and advancement of topological strings and topological phases of quantum electronic matter. The project focuses on, but is not limited to, electronic condensed matter systems in three spatial dimensions, where quantum and collective behaviors of strings are largely unexplored. Topological phases support unconventional emergent particles or strings, which act radically different from the constituent fundamental particles. Fractionally charged quasiparticles in a fractional quantum Hall state are perfect examples. Topological strings are quasi-one-dimensional objects that emerge from a nontrivial environment, like a vortex line in a superconductor, and can exhibit technologically desirable characteristics, such as dissipationless fractional and separated transport of energy, spin, and charge. The research concentrates on three correlated main objectives. First, it broadens the current understanding of topological line defects to facilitate realization in topological materials. This includes the discovery of new classes of natural or designed materials that support topological strings. The goal is achieved by a systematic characterization and classification of novel strings in these previously unexplored systems. Second, it examines the collective properties of interacting strings, and develops mesoscopic model descriptions of topological phases in three dimensions. This involves both analytic and numerical studies of many-body interacting networks of topological strings. Third, it expands the topological field-theoretical narrative of topological phases in 3+1 dimensions, and aims to unearth new quantum dynamical string behaviors. This is accomplished by applying the mathematical theory of knots and links in new categories of quantum cyclic evolution of entangled strings. This research project has significant potential impact not only on the condensed matter community, but also on materials science and engineering, on high-energy physics, and even on pure mathematics. It has the potential to open new frontiers in the theory of electronic matter, and in the realization of new topological materials and technological applications such as a quantum computer. This award also supports broader educational activities: The PI will continue mentoring and training graduate students, including members of underrepresented groups, in advanced theoretical methods. In addition, he will participate in outreach efforts targeting local high schools, and will help connect the general public with scientific research through public talks and physics demonstrations.