Introduction to the theory of topological insulators

by Prof. David Vanderbilt (Rutgers University)

Tuesday 15 Jul 2014, 16:00 → 17:00 Asia/Kolkata

AG69 (Colaba Campus)

One of the "hot topics" in condensed-matter theory in the last decade has been the discovery and investigation of so-called "topological insulators" (TIs). Heuristically speaking, these are materials whose ground-state electron wavefunctions wrap around the Brillouin zone with a "twist" that cannot be removed without closing the band gap. In this talk, I will first give an introduction to Berry phases and curvatures, mathematical objects that are essential for describing the topological states in question. I will then give a brief survey of the different types of topological states that are currently of such interest, including quantum anomalous Hall (QAH) and quantum spin Hall (QSH) systems in 2D, and strong and weak TIs in 3D. Finally, I will briefly review some of our own recent work in which we propose the deposition of atoms with strong spin-orbit interactions onto the surfaces of magnetic insulators as a promising route toward the synthesis of QAH systems. These hold promise to reproduce the physics of the famous quantum Hall effect, but without the usual constraints of low temperature and applied magnetic field.