Topology and Condensed Matter Physics

ABOUT THE COURSE :The study of Condensed Matter Physics is no longer the same after a series of important discoveries in the eighties of the earlier century. It has digressed from conventional topics to the emergence of a topological order that is found to be responsible for a number of exotic features, such as Quantum Hall effect, electronic and transport properties of Graphene and Weyl semi-metals etc. This course gives an overview of topological implications in the field of condensed matter and material science and will be very crucial to students who wish to join PhD in the field. Also, for the enthusiastic teachers, who teach solid state physics at the undergraduate or the graduate level, this course will render a novel viewpoint to the experiments and theory.INTENDED AUDIENCE : M.Sc, PhD Students and researchers from institutes and universities. Faculty members intending to teach Condensed Matter Physics at the graduate or post graduate level.PREREQUISITES : Quantum mechanics, Solid State Physics.

Week 1: Introduction to Topology, Relevance of topology in Condensed Matter Physics, symmetry and topologyWeek 2:Ten-fold way, periodic table of topological insulators, overview of topological materials.Week 3:Topological invariants, Berry curvature, Chern number, Quantum Hall effect, Hofstadter modelWeek 4:SSH Model, Kitaev model, Majorana fermions, Bulk boundary correspondenceWeek 5:Two dimensional topological materials, Graphene, Haldane model, Half-BHZ Model, Kane Mele model, edge modesWeek 6:Quantum spin Hall effect, experimental discovery of strained semiconductors, band inversionWeek 7:Three dimensional topological insulators, Weyl semi metalsWeek 8:Experimental discovery and progress of Topological insulators