CAREER: Novel Quantum Hall and Correlation Physics in Topological Band Structures

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TECHNICAL SUMMARYThis CAREER award supports theoretical research and education to investigate the new quantum Hall and correlation physics in materials involving topological band structures. Using quantum field theory, variational Monte Carlo, exact diagonalization and other modern quantum many-body techniques, the PI will pursue four main research directions:(1) Exploring novel phases of matter in transition metal oxide heterostructures, where various topological phases may emerge. These include possible high-temperature quantum spin hall phases and correlation induced fractional quantum hall phases in the absence of an external magnetic field.(2) Understanding the nature of the abelian and non-abelian fractional Chern insulators and topological insulators. The research will focus on constructing wavefunctions for these states and understanding their low energy properties.(3) Investigating correlated quantum Hall effects of the 2D Dirac surface states of a 3D topological insulator. (4) Understanding the quantum Hall effects and experimental signatures of 3D Weyl semi-metal phases, which may be realized in materials such as pyrochlore iridates.The educational activities associated with this award include developing pedagogical courses and a seminar series for undergraduate and graduate students, with emphasis on the new phases of matter discovered in modern condensed matter physics. These are intended to excite students to study and actively pursue research in physics. Outreach activities include a lecture series aimed at sparking the interest in science and technology among middle school students, especially in low-income areas. These lectures are designed to expose the young audience to some striking advances in the history of modern science and technology, and their roles in our everyday life. To generate interest in science over a broader scale, the PI will develop an interactive website for hosting an overview of his research activities as well as teaching materials. NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to investigate a recently discovered new state of electronic matter that arises in certain materials called topological insulators. Materials are often classified according to the ways electrons organize themselves within the material, leading to materials types that include: metals if they conduct electricity, insulators if they do not, and the familiar magnet. Fundamental concepts make this classification even more precise. Topological insulators lie outside this traditional classification scheme making them very important from a fundamental science perspective. They are at once an insulator in the bulk of the material, but unlike an ordinary insulator that forms the basis of modern electronics, there is a metal-like state on the surfaces and edges of the insulator. The metal-like state is an intrinsic property of the material that is a consequence of the way electrons in the bulk organize themselves. This state hosts striking phenomena such as ideal electric transport on the boundaries of the material without losing any energy. This project focuses on answering fundamental scientific questions about topological insulators: What are the fundamental properties of these topological phases? How can they be found in practical materials? What are their potential applications? The PI will also investigate many promising candidate materials for topological phases, and the effect of an external magnetic field on these phases. The conducting surfaces of topological insulators and the possibility of new phenomena that occur when a topological insulator is brought into contact with other materials, suggests many possible technological applications from new device technologies to high performance computer technologies based on the manipulation of quantum mechanical states. The educational activities associated with this award include developing pedagogical courses and a seminar series for undergraduate and graduate students, with emphasis on the new phases of matter discovered in modern condensed matter physics. These are intended to excite students to study and actively pursue research in physics. Outreach activities include a lecture series aimed at sparking the interest in science and technology among middle school students, especially in low-income areas. These lectures are designed to expose the young audience to some striking advances in the history of modern science and technology, and their roles in our everyday life. To generate interest in science over a broader scale, the PI will develop an interactive website for hosting an overview of his research activities as well as teaching materials.