Journal
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL
Volume 47, Issue 15, Pages -Publisher
IOP PUBLISHING LTD
DOI: 10.1088/1751-8113/47/15/152001
Keywords
fractional Chern insulator; electronic band structure; topology; invariants; tight binding models; K-theory
Categories
Funding
- NSF [DMR-1206781, 0900985]
- NSA [H96230-13-1-02]
- Direct For Mathematical & Physical Scien
- Division Of Materials Research [1206781] Funding Source: National Science Foundation
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [0900985] Funding Source: National Science Foundation
Ask authors/readers for more resources
We investigate the possibility of exactly flat non-trivial Chern bands in tight binding models with local (strictly short-ranged) hopping parameters. We demonstrate that while any two of the three criteria can be simultaneously realized (exactly flat band, non-zero Chern number, local hopping), it is not possible to simultaneously satisfy all three. Our theorem covers both the case of a single flat band, for which we give a rather elementary proof, as well as the case of multiple degenerate flat bands. In the latter case, our result is obtained as an application of K-theory. We also introduce a class of models on the Lieb lattice with nearest and next-nearest neighbor hopping parameters, which have an isolated exactly flat band of a zero Chern number but, in general, non-zero Berry curvature.
Authors
I am an author on this paper
Click your name to claim this paper and add it to your profile.
Reviews
Recommended
No Data Available