APS March Meeting 2011
Volume 56, Number 1
Monday–Friday, March 21–25, 2011;
Dallas, Texas
Abstract: Y2.00005 : Classification of Topological Insulators and Superconductors: the ``Ten-Fold Way''
10:24 AM–11:00 AM
Preview Abstract
Author:
We review the exhaustive ten-fold classification scheme of
topological insulators and
superconductors. It is found that the conventional (i.e.:
``$Z_2$'', or `spin-orbit')
topological insulator, experimentally observed in 2D (`Quantum
Spin Hall') and in 3D materials,
is one of a total of five possible classes of topological
insulators or superconductors which exist
in every dimension of space.
Different topological sectors within a given class can be
labeled, depending on the case, by an integer
winding number, or by a ``binary'' $Z_2$ quantity. The topological
nature of the bulk manifests itself through
the appearance of ``topologically protected'' surface states.
These surface states completely evade
the phenomenon of Anderson localization due to disorder.
Examples of the additional topological phases in 3D include
topological superconductors (i) with spin-singlet
pairing, and (ii) with spin-orbit interactions, as well as
${}^{3}{\rm He \ B}$. --
The classification of topological insulators (superconductors) in
d dimensions is reduced to
the problem of classifying Anderson localization at the
(d-1)-dimensional sample boundary
which, in turn, is solved.
The resulting five symmetry classes of topological insulators
(superconductors) found to
exist in every dimension of space correspond to a certain subset
of five of the ten generic symmetry
classes of Hamiltonians introduced 16 years ago by Altland and
Zirnbauer in the context of
disordered systems (generalizing the three well-known
``Wigner-Dyson'' symmetry classes).
For a significant part of the phases of topological insulators
(superconductors)
of the classification a characterization can be given in terms of
the
responses of the system. For these, the responses are described
by a field theory possessing
a [gauge, gravitational (thermal), or mixed] anomaly. This
implies that these phases are well defined also in the presence
of inter-fermion interactions.
To cite this abstract, use the following reference: http://meetings.aps.org/link/BAPS.2011.MAR.Y2.5