PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Mathieu Stienon, Nigel Higson, Ping Xu.

Title:Periodic table for topological insulators and superconductors
Seminar:GAP Seminar
Speaker:Alexei Kitaev, CalTech
Abstract:
Professor Kitaev will elaborate on his physics talk earlier this week. In particular, he will give exact definitions of the key objects and sketch a proof of a theorem he mentioned, which is a kind of controlled K-homology where matrices and epsilon-delta arguments are used instead of infinite Hilbert spaces. Abstract of his earlier talk: Gapped phases of noninteracting fermions, with and without charge conservation and time-reversal symmetry, are classified using Bott periodicity. The symmetry and spatial dimension determines a general universality class, which corresponds to one of the 2 types of complex and 8 types of real Clifford algebras. The phases within a given class are further characterized by a topological invariant, an element of some Abelian group that can be 0, Z, or Z_2. The interface between two infinite phases with different topological numbers must carry some gapless mode. Topological properties of finite systems are described in terms of K-homology. This classification is robust with respect to disorder, provided electron states near the Fermi energy are absent or localized. In some cases (e.g., integer quantum Hall systems) the K-theoretic classification is stable to interactions, but a counterexample is also given.

Room Reservation Information

Room Number:MB106
Date:03 / 17 / 2009
Time:02:30pm - 03:30pm