# Periodic table for topological insulators and superconductors

## GAP Seminar

## Meeting Details

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

**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:** 106 McAllister

**Date:** 03/17/2009

**Time:** 2:30pm - 3:30pm