The Role of Gauge Symmetries in the Discovery of Novel States of Condensed Matter

Jürg Fröhlich

em., ETH Zürich/IAS Princeton Cambridge, October 29, 2012

A short summary of my lecture

Credits: Bieri, Boyarsky, Cheianov, Graf, Kerler, Levkivskyi, Pedrini, Ruchayskyi, Schweigert, Studer, Sukhorukov, Thiran, Walcher, Werner, Zee – R. Morf Period of work: 1989/90 – 2012 (from postmodern to modern), with many interruptions

Remarks on experimental realizations: - Spin quantum Hall effect observed in materials with strong spin-orbit coupling and “inverted band gap” Example: HgTe (Würzburg group – Molenkamp et al.) - 3D topological insulators realized in Bi2Te3 , Bi2Se3,, etc. (insulators with spin-orbit coupling and “inverted band gaps”; materials with magnetic fluctuations axionic topological insulators)

- Cold atom gases in an effective external gauge field

Some digressions for people in the audience interested in theory 1) Theoretical ideas

concerning the classification of incompressible Hall fluids exhibiting the quantum Hall effect; or

2) Higher-dimensional cousins of the quantum Hall effect, with applications to cosmology