The Stiefel--Whitney theory of topological insulators
Kaufmann, Ralph M. ; Li, Dan ; Wehefritz-Kaufmann, Birgit
arXiv, 1604.02792 / Harvested from arXiv
Text on arXiv
We study the topological band theory of time reversal invariant topological insulators and interpret the topological $\mathbb{Z}_2$ invariant as an obstruction in terms of Stiefel--Whitney classes. The band structure of a topological insulator defines a Pfaffian line bundle over the momentum space, whose structure group can be reduced to $\mathbb{Z}_2$. So the topological $\mathbb{Z}_2$ invariant will be understood by the Stiefel--Whitney theory, which detects the orientability of a principal $\mathbb{Z}_2$-bundle. Moreover, the relation between weak and strong topological insulators will be understood based on cobordism theory. Finally, the topological $\mathbb{Z}_2$ invariant gives rise to a fully extended topological quantum field theory (TQFT).
Publié le : 2016-04-11
Classification:  Mathematical Physics 
@article{1604.02792,
     author = {Kaufmann, Ralph M. and Li, Dan and Wehefritz-Kaufmann, Birgit},
     title = {The Stiefel--Whitney theory of topological insulators},
     journal = {arXiv},
     volume = {2016},
     number = {0},
     year = {2016},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1604.02792}
}

Kaufmann, Ralph M.; Li, Dan; Wehefritz-Kaufmann, Birgit. The Stiefel--Whitney theory of topological insulators. arXiv, Tome 2016 (2016) no. 0, . http://gdmltest.u-ga.fr/item/1604.02792/