Topology and Superconductivity In and Out of Equilibrium

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The field of condensed matter physics is concerned with understanding and controlling the properties of materials. Material properties are determined by the microscopic components of matter - electrons and atoms. The microscopic world is governed by the laws of quantum mechanics, rather than classical mechanics and is described mathematically with tools specifically developed for systems of many particles (of the order of 10^22 atoms per cubic cm). Such tools have existed for over 60 years and have been very successful in predicting properties like conduction and magnetism from microscopic considerations. In particular, Landau's Fermi liquid theory describes the electrons as they move through an ordered lattice of atoms. In this framework very general arguments allow physicists to classify states of matter and study transitions between different states. ******However, thanks to advances over the past decade, we now know that some materials do not match any of the previously proposed classes. To be more precise, the classification should be refined. While the 'old' classification of matter is based on the notion of symmetry - invariance of the system under some coordinate transformation (like time reversal, spin rotation, point group), the new classification should include topological aspects as well as symmetry considerations. For example, new materials which were discovered recently are called topological insulators and topological superconductors. They can be distinguished from non-topological insulators and superconductors by their topology but not by their symmetry. The topology also has physical consequences. Most notably, topological insulators have an insulating bulk while maintaining conducting states on their surfaces. .******With the help of the discovery grant I will continue to pursue the study of topological states of matter. I'm particularly interested in driving systems into and out of topological states using external fields. In particular, one can apply a time dependent electromagnetic field (like light) and drive the system out of thermal equilibrium. The non-equilibrium system may be different from the un-driven system and may posses different topological properties. ******My work is theoretical and will focus on predicting the properties of materials and devices and proposing feasible experiments. Once topological properties can be controlled by applying external fields many applications in the field of electronics and spintronics may follow.