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The K-theoretic bulk-edge correspondence for topological insulators

Journal Article


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Abstract


  • We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real (Formula presented.)-algebras and KKO-theory must be used.

Authors


  •   Bourne, Christopher J. (external author)
  •   Kellendonk, Johannes (external author)
  •   Rennie, Adam C.

Publication Date


  • 2017

Citation


  • Bourne, C., Kellendonk, J. & Rennie, A. (2017). The K-theoretic bulk-edge correspondence for topological insulators. Annales Henri Poincare, Online First 1-34.

Scopus Eid


  • 2-s2.0-85008144275

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7397&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6367

Number Of Pages


  • 33

Start Page


  • 1

End Page


  • 34

Volume


  • Online First

Abstract


  • We study the application of Kasparov theory to topological insulator systems and the bulk-edge correspondence. We consider observable algebras as modelled by crossed products, where bulk and edge systems may be linked by a short exact sequence. We construct unbounded Kasparov modules encoding the dynamics of the crossed product. We then link bulk and edge Kasparov modules using the Kasparov product. Because of the anti-linear symmetries that occur in topological insulator models, real (Formula presented.)-algebras and KKO-theory must be used.

Authors


  •   Bourne, Christopher J. (external author)
  •   Kellendonk, Johannes (external author)
  •   Rennie, Adam C.

Publication Date


  • 2017

Citation


  • Bourne, C., Kellendonk, J. & Rennie, A. (2017). The K-theoretic bulk-edge correspondence for topological insulators. Annales Henri Poincare, Online First 1-34.

Scopus Eid


  • 2-s2.0-85008144275

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=7397&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/6367

Number Of Pages


  • 33

Start Page


  • 1

End Page


  • 34

Volume


  • Online First