CAREER: Advancing the Many-body Band Inversion Paradigm for Correlated Quantum Materials

Drexel University, Philadelphia PA

Investigators

Abstract

NONTECHNICAL SUMMARY This CAREER award supports theoretical research and education in the rapidly developing field of materials physics known as quantum materials. Quantum materials have properties and exhibit phenomena deeply rooted in the laws of quantum physics, thus providing a key resource for future quantum-based technologies. This project specifically focuses on a particularly prominent example of such materials, the topological materials. The remarkably robust electronic properties of topological materials can be understood with the help of abstract mathematical concepts derived from the study of geometry and shape. When the electrons in these materials are strongly interacting, surprising and exotic phenomena can occur. Understanding these phenomena and the fundamental principles that govern them is a key step towards new energy and computing technologies. The goal of this project is to advance a new paradigm for describing and understanding such strongly interacting materials, and thereby to provide a new perspective for materials discovery. The research activities will build on recent work of the PI, which introduced a formalism for describing systems of interacting electrons that fall outside the currently predominant paradigm for understanding strong interactions. This formalism opens the door to new insight into fundamental properties and behavior of matter, in particular the properties of exotic quantum states, and serves to identify materials in which these are realized. This project will systematically develop and extend the proposed formalism, focusing on systems and materials in two and three dimensions with different structure, chemistry, and symmetry properties. Conceptual advances will be leveraged to provide new pathways to materials prediction and discovery, with the aim of enabling experimental progress on the frontier of correlated topological quantum states. Quantum materials appear to be at the epicenter of next-generation technological innovation, while at the same time offering unique insight into the fundamental building blocks of matter. This award also supports activities in the areas of education and outreach designed to increase the visibility of quantum materials research and to broaden participation in condensed matter physics. These activities contribute to the workforce in quantum materials and technologies. Supported initiatives include: (i) building a professional development certificate program in quantum technology open to non-physicists, (ii), launching an in-house quantum materials summer school as incubator for collaboration (iii), offering diverse and inclusive pre-graduate research opportunities and (iv) expanding the reach and visibility of condensed matter physics through an outreach program for undergraduates. TECHNICAL SUMMARY This CAREER award supports theoretical research and education in the rapidly developing field of quantum materials, with a specific focus on strongly correlated topological quantum materials. Topological materials are a new class of quantum materials which have exposed a deep connection between abstract mathematical concepts, for example the topology of wave functions, and physical material properties, for example the presence of intrinsically robust transport channels. Our understanding of topological materials relies on one of the central pillars of the modern band theory of solids: the notion of a band inversion. Given its remarkable success in advancing our knowledge of metals and insulators, the goal of this project is to develop a generalization of the band inversion paradigm to strongly interacting topological quantum states. This many-body band inversion paradigm offers a wave function-based approach to studying the structure, properties, and function of strongly correlated topological quantum phases in quantum materials. It overcomes limitations inherent in the flat-band paradigm inspired by the quantum Hall effect and offers a new materials perspective for identifying materials which may realize exotic correlated quantum states. The research activities are organized in three interrelated and complementary research thrusts. The first thrust will focus on systems in two dimensions. Computational methods will be employed to map out the phase diagram in model systems for real materials near a correlated band inversion transition. In addition, existing experimental work on correlated topological semimetals will be examined. The second thrust is concerned with systems in three dimension, in particular band-inverted topological semimetals with higher angular momentum and presents a pathway to generalizing the many-body band inversion to three dimensions. The third thrust is informed by the insight of the first two thrusts and suggests a materials platform for realizing strongly correlated topological ground states at a band inversion transition. These thrusts advance the common goal of uncovering new correlated topological phases outside of the current paradigm. This award also supports activities in the areas of education and outreach. These activities are tightly integrated with the proposed research and harness the ascendance of quantum materials as a key resource for future technology. Supported initiatives include: (i) building a professional development certificate program in quantum technology open to non-physicists, (ii), launching an in-house quantum materials summer school as incubator for collaboration (iii), offering diverse and inclusive pre-graduate research opportunities and (iv) expanding the reach and visibility of condensed matter physics through an outreach program for undergraduates. 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.