This CAREER award supports theoretical research and education to investigate quantum mechanical states of electrons in materials and transformations among them that require new theoretical concepts for their description. Experimental discoveries and theoretical advances reveal novel properties and electronic states of matter that lie outside the standard conceptual framework used to describe the transformation from one state of matter into another, and used to describe the state of electrons that interact strongly with each other in materials. To advance understanding of these and other predicted new states of matter and the transformations among them, the PI will focus on three major activities: (1) developing theoretical and computational tools to understand what happens as physical conditions are changed to drive transformations between phases that owing to the collective behavior of the electrons appear to be made of particles with a charge that is a fraction of a fundamental electron charge; (2) developing theoretical models to advance understanding of a fundamentally new kind of material system, in which a 3 dimensional material hosts interesting electric states that exist only at the boundaries; and (3) proposing new experiments that can detect fractional particles that are predicted to occur in specially engineered materials. The research provides simulating training for graduate students. The PI will help convey the excitement of materials research through outreach activities aimed at inspiring interest in the science among students at the secondary school level. In collaboration with local high-school teachers, as well as students, the PI will develop web-based learning tools allowing students to explore the materials science underlying many of the technologies familiar from daily life. The objective is to allow students to explore at their own pace and in an intuitive, rather than mathematical, way some of the more astonishing properties of systems of many interacting quantum particles, such as superconductivity, and emergence of particles with charges that are a fraction of an electron charge.
This CAREER award supports theoretical research and educational activities focused on understanding phases of matter beyond the Landau paradigm; systems whose physics cannot be fully understood either by Fermi liquid theory, or by considering possible symmetry-breaking ordered states. Specifically, this project focuses on two types of phenomena not captured by either of these frameworks: topological order in 1D and 2D, and symmetry protection in strongly interacting 3D systems. The research has three main components: 1.) To advance understanding of the phase diagrams and phase transitions in 2D topologically ordered systems. The PI plans to build on existing numerical and theoretical tools to better understand criticality between phases of different topological order in 2D. These transitions are interesting and challenging to study because the topological character of the critical degrees of freedom implies that no local order parameter exists, and fundamentally new tools are needed. Experimentally realistic systems where such transitions occur will be sought. 2.) To advance understanding of strongly interacting symmetry-protected phases in 3D, the PI will develop theoretical models and identify the relevant field theories. The particular focus will be on the topological character of defects and surface states in these strongly interacting systems, building on methods applied successfully to non-interacting systems. 3.) The PI aims to quantify new experimental probes that can help identify excitations with non-abelian statistics. Recent proposals for realizing these in new ways in the laboratory have raised the challenge of understanding feasible and reliable detection techniques for these systems. The research will build on existing knowledge of how finite-frequency responses in these systems characterize their topological nature. The research provides simulating training for graduate students. The PI will help convey the excitement of materials research through outreach activities aimed at inspiring interest in the science among students at the secondary school level. In collaboration with local high-school teachers, as well as students, the PI will develop web-based learning tools allowing students to explore the materials science underlying many of the technologies familiar from daily life. The objective is to allow students to explore at their own pace and in an intuitive, rather than mathematical, way some of the more astonishing properties of systems of many interacting quantum particles, such as superconductivity, and emergence of particles with charges that are a fraction of an electron charge.
