Universität zu Köln

Kennedy, R. and Zirnbauer, M. R. (2015). Bott-Kitaev periodic table and the diagonal map. Phys. Scr., T164. BRISTOL: IOP PUBLISHING LTD. ISSN 1402-4896

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Abstract

Building on the ten-way symmetry classification of disordered fermions, the authors have recently given a homotopy-theoretic proof of Kitaev's 'periodic table' for topological insulators and superconductors. The present paper offers an introduction to the physical setting and the mathematical model used. Basic to the proof is the so-called diagonal map, a natural transformation akin to the Bott map of algebraic topology, which increases by one unit both the momentum-space dimension and the symmetry index of translation-invariant ground states of gapped free-fermion systems. This mapping is illustrated here with a few examples of interest. (Based on a talk delivered by the senior author at the Nobel Symposium on 'New Forms of Matter: Topological Insulators and Superconductors'; Stockholm, 13-15 June, 2014.)

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kennedy, R. UNSPECIFIED UNSPECIFIED UNSPECIFIED Zirnbauer, M. R. UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-384932
DOI:	10.1088/0031-8949/2015/T164/014010
Journal or Publication Title:	Phys. Scr.
Volume:	T164
Date:	2015
Publisher:	IOP PUBLISHING LTD
Place of Publication:	BRISTOL
ISSN:	1402-4896
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Physics, Multidisciplinary Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/38493