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Topological Invariants for Disordered Topological Insulators

Event Details

Event Dates: 

Thursday, November 1, 2012 - 6:00am

Speaker Name(s): 

Matt Hastings

Speaker Affiliation(s): 

Duke University/Station Q
Seminar Type/Subject

Event Details & Abstract: 

The term "topological insulator" refers to several different classes of free fermion systems whose nontrivial topological properties lead to interesting observable effects such as edge modes.  The integer quantum Hall effect is now understood to be the earliest such class to be discovered, but now there is a systematic classification of these systems in different dimensions and with different symmetries.   Some of these are experimentally realized including the most famous example, the time-reversal invariant topological insulator in two dimensions.  I'll present an approach to classifying these systems based on methods from a branch of mathematics called C*-algebra.  The advantage of this method is both that it will allow simple proofs that certain quantities indeed are topological invariants, even for disordered systems, and that it leads to fast numerical algorithms for calculating these invariants.  (Joint work with T. Loring)