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H 1 Topological nature of the Fu-Kane-Mele invariants

Auteurs : De Nittis, Giuseppe (Auteur de la Conférence)
CIRM (Editeur )

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    Résumé : Condensed matter electronic systems endowed with odd time-reversal symmetry (TRS) (a.k.a. class AII topological insulators) show topologically protected phases which are described by an invariant known as Fu-Kane-Mele index. The construction of this in- variant, in its original form, is specific for electrons in a periodic background and is not immediately generalizable to other interesting physical models where different forms of TRS also play a role. By exploiting the fact that system with an odd TRS (in absence of disorder) can be classified by Quaternionic vector bundles, we introduce a Quaternionic topological invariant, called FKMM-invariant, which generalizes and explains the topological nature of the Fu-Kane-Mele index. We show that the FKMM-invariant is a universal characteristic class which can be defined for Quaternionic vector bundles in full generality, independently of the particular nature of the base space. Moreover, it suffices to discriminate among different topological phases of system with an odd TRS in low dimension. As a particular application we describe the complete classification over a big class of low dimensional involutive spheres and tori. We also compare our classification with recent results concerning the description of topological phases for two-dimensional adiabatically perturbed systems.
    Joint work with: K. Gomi.

    Codes MSC :
    19L64 - Computations, geometric applications
    53C80 - Applications of global differential geometry to physics
    55N25 - Homology with local coefficients, equivariant cohomology
    57R22 - Topology of vector bundles and fiber bundles

      Informations sur la Vidéo

      Langue : Anglais
      Date de publication : 04/05/16
      Date de captation : 19/04/16
      Collection : Research talks ; Mathematical Physics
      Format : MP4
      Durée : 01:00:16
      Domaine : Mathematical Physics
      Audience : Chercheurs ; Doctorants , Post - Doctorants
      Download : https://videos.cirm-math.fr/2016-04-19_de_Nittis.mp4

    Informations sur la rencontre

    Nom de la rencontre : Spectral theory of novel materials / Théorie spectrales des nouveaux matériaux
    Organisateurs de la rencontre : Exner, Pavel ; Kotani, Motoko ; Kuchment, Peter ; Zagrebnov, Valentin A.
    Dates : 18/04/2016 - 22/04/2016
    Année de la rencontre : 2016
    URL Congrès : http://conferences.cirm-math.fr/1399.html

    Citation Data

    DOI : 10.24350/CIRM.V.18962003
    Cite this video as: De Nittis, Giuseppe (2016). Topological nature of the Fu-Kane-Mele invariants. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18962003
    URI : http://dx.doi.org/10.24350/CIRM.V.18962003


    Voir aussi

    Bibliographie

    1. De Nittis, G., & Gomi, K. (2016). Topological nature of Fu-Kane-Mele invariants. - http://arxiv.org/abs/1603.09421

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