This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).
This award supports theoretical research and education in theoretical condensed matter physics. Three broad topics will be studied: (1) electronic properties of topological insulators and related materials, (2) topological band theory, and (3) methods for probing Majorana fermions in condensed matter systems. For each of these topics the proposed work will explore the interplay between topological aspects of band theory, disorder and interactions. The first topic is motivated by recent developments which have demonstrated the existence of a new class of insulating materials dubbed topological insulators. Two key experiments recently observed this effect in two dimensional Hg(1-x)CdxTe quantum well structures and three dimensional Bi(1-x)Sbx crystals. The second topic seeks to generalize the topological classification of insulating band structures to account for other symmetries, such as particle-hole symmetry (as in a superconductor) as well as spatial symmetries. This is expected to lead to a richer set of topological classifications, and it will be of interest to explore the physical consequences of these topological classes, and to physically characterize new phases which emerge. The third topic seeks to develop a methods for experimentally probing Majorana fermions using topological insulators. Bound states of Majorana fermions are interesting now because they can form the building blocks for a topological quantum computer, which can process and store quantum information in a way which is immune from local sources of decoherence.
The broader impact of the proposed work involves both the potential for technological innovation and the development of human resources. Topological insulators have potential to provide a basis for new classes of electronic devices, both in the field of spintronics and more ambitiously in the field of quantum omputation. The problems in this proposal will also be an ideal arena for training a graduate student in the modern methods of condensed matter theory. The PI also plans to develop a series of lectures for sophomore undergraduates with the goal of introducing the students to notions of topology in physics.
NON-TECHNICAL SUMMARY: This award supports theoretical research and education in condensed matter physics. The PI aims to further study a new kind of insulator predicted by theory. It has long been known that insulators do not conduct electric current. In the past 5 years, theory predicted that certain insulating materials could give rise to a new state of matter. These materials remain insulating in the bulk, but are able to support a metallic state on the surfaces that can conduct electricity without dissipation. This new state of matter has intriguing, exciting, and unusual properties. In a sense it is analogous to states of matter that arise when electrons are trapped in two dimensions and exposed to a high magnetic field perpendicular to the plane. The PI will use theoretical methods to explore this and other new states of matter with an eye toward devising and proposing experimental tests to uncover their intriguing properties.
New states of matter may open new technologies, particularly electronic device and information technologies, which contribute to competitiveness of America. Realizing these possibilities requires solid theoretical understanding. The discovery of new states of matter and their exploration is potentially transformative. The research also provides ideal educational experiences for graduate students to train them in modern methods of condensed matter theory. The PI also plans to develop a series of lectures for sophomore undergraduates with the goal of introducing them to how advanced mathematical concepts can help us understand physical world around us.
