CAREER: The Fate of Topology in Disordered Three-Dimensional Materials

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

NONTECHNICAL ABSTRACT This CAREER award supports research and educational activities in the study of new topological states of matter. Electrons in some materials self-organize into topological states of matter which are predicted to exist from the application of new ideas forged from the fusion of concepts from theoretical condensed matter physics and topology, the branch of mathematics that describes the properties of objects that remain unchanged under deformation, twisting, and bending. The existence of these states leads to intriguing quantum mechanical properties that are unaffected by small changes in the material. Dissipationless electrical conduction channels and bulk insulators that are spontaneously covered by essential metallic states at their surfaces and edges are among the interesting features of topological materials. They hold promise for future technological application in electronics, spintronics and quantum computers. However, all materials have imperfections, impurities, and defects, together referred to as disorder. This research project will focus on the interplay of disorder and topology in three-dimensional materials. The properties of topological materials are insensitive to disorder, but they are not immune. This project is aimed to advance understanding of the effects of disorder in topological materials and to determine the appropriate protocols for robust and practical applications in electronic devices, quantum computers and other technologies. In order to develop an internationally competitive technical workforce, it is essential to educate the next generation of scientists. The principal investigator will help achieve this goal by developing a strong mentorship program that includes students that are K-12, undergraduate, and graduate, as well as postdoctoral scholars. The PI will provide graduate students and postdocs with professional development experiences through research and exposure to industrial job opportunities. Lastly, the PI will develop powerful open source scientific software that will be made freely accessible in order to study disordered topological materials. TECHNICAL ABSTRACT This CAREER award supports research and education in theoretical condensed matter physics focusing on the interplay of disorder, strong correlation, and topology in three-dimensional quantum phases of matter. Topological materials hold great promise for future technological applications ranging from low-loss electronics to quantum computers. However, all materials contain disorder and it is therefore essential to ascertain what useful topological properties remain robust away from the idealized clean limit. Therefore, the objectives of this research activity are threefold: (1) Determine if non-perturbative effects of disorder generically destabilize the quantum critical point that separates three-dimensional topological and trivial insulators into a metallic phase. (2) Develop an efficient numerical method to compute nonlinear optical responses to detect and characterize topological properties of three-dimensional materials. (3) Determine if disorder affects the formation of emergent topological band structures in strongly correlated materials. The PI will employ large scale numerical calculations that utilize the kernel polynomial method and diagonalization techniques to efficiently simulate large lattice models without translational symmetry. This research activity utilizes a cross fertilization of ideas from statistical physics, topological field theories, critical phenomena, and computational physics. The ultimate goal of this research is to determine how disorder fundamentally alters gapless topological phases of matter. The planned fundamental research will help to establish the theoretical framework for evaluating the impact of disorder on gapless topological phases of matter, which will quantify the required levels of purity for use in technological applications. The PI’s education plan aims to develop a competitive technical workforce through active mentorship, research opportunities, meeting with industry partners, and developing open source scientific software. In particular, the PI’s education activities will focus on three main areas: (1) The PI will integrate research with teaching through mentorship to improve STEM education for students from K-12, undergraduates, and graduates, as well as postdoctoral scholars. (2) The PI will develop a diverse, competitive workforce by fostering graduate student professional development through a combination of research exposure and industry exchanges. (3) The PI will develop an open source scientific software package to simulate disordered quantum systems that is made publicly available to enhance the infrastructure for research and education. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.