What do we learn?
This advanced course covers the fundamentals of the thriving field of Topological States of Matter. We discuss both theoretical and experimental aspects and emphasize the physical picture over the technical details. The course is divided to nine units: The Integer and Fractional Quantm Hall Effects are covered in the first unit, including the concepts of edge states, localization, fractional charges, composite fermions, and non-abelian states; Topological Superconductivity is covered in the 2nd unit, including the concepts of the Thouless pump, Majorana zero modes, and realizations in one and two dimensions; Topological Universe on a Graphene Sheet is offered by the 3rd unit, including the concepts of Dirac cones, Klein tunneling and Chern bands, as well as the rich world of twisted bi-layer graphene; Topological Insulators are covered by the 4th unit, including two- and three- dimensional systems, as well as topological crystalline insulators; The 5th unit, on Topological Classification, puts all examples of the previous units into a unified framework, introducing the periodic table of gapped topological systems with no topological order; The 6th unit expands the course into the realm of Gapless Topological Phases, covering Dirac and Weyl semi-metals, both in their bulk and surface; The 7th unit covers the theoretical tools for Predicting Topological Materials, with an emphasis on Density Functional Theory, and the quantities that need to be calculated to probe the topological characteristics of a material; The 8th unit dives into the abstract world of Topological Order, from the Toric Code all the way to a brief discussion of Topological Quantum Computation; And finally, the 9th unit describes some Experimental Tools that are of wide use in the study of topological states of matter, and makes connection between measurements and their interpretation.
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