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Kennedy, Ricardo and Guggenheim, Charles (2015). Homotopy theory of strong and weak topological insulators. Phys. Rev. B, 91 (24). COLLEGE PK: AMER PHYSICAL SOC. ISSN 2469-9969

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Abstract

We use homotopy theory to extend the notion of strong and weak topological insulators to the nonstable regime (low numbers of occupied/empty energy bands). We show that for strong topological insulators in d spatial dimensions to be truly d-dimensional, i.e., not realizable by stacking lower-dimensional insulators, a more restrictive definition of strong is required outside the stable regime. However, this does not exclude weak topological insulators from being truly d-dimensional, which we demonstrate by an example. Additionally, we prove some useful technical results, including the homotopy theoretic derivation of the factorization of invariants over the torus into invariants over spheres in the stable regime, as well as the rigorous justification of the parameter space replacements T-d -> S-d and T-dk x S-dx -> Sdk+dx used widely in the current literature.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Kennedy, Ricardo UNSPECIFIED UNSPECIFIED UNSPECIFIED Guggenheim, Charles UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-400929
DOI:	10.1103/PhysRevB.91.245148
Journal or Publication Title:	Phys. Rev. B
Volume:	91
Number:	24
Date:	2015
Publisher:	AMER PHYSICAL SOC
Place of Publication:	COLLEGE PK
ISSN:	2469-9969
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language SINGLE DIRAC CONE; PHASE-TRANSITION Multiple languages Materials Science, Multidisciplinary; Physics, Applied; Physics, Condensed Matter Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/40092