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Momentum-space instantons and maximally localized flat-band topological Hamiltonians

Jian, Chao-Ming and Gu, Zheng-Cheng and Qi, Xiao-Liang (2013) Momentum-space instantons and maximally localized flat-band topological Hamiltonians. Physica Status Solidi - Rapid Research Letters, 7 (1-2). pp. 154-156. ISSN 1862-6254. doi:10.1002/pssr.201206394.

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Recently, two-dimensional band insulators with a topologically nontrivial (almost) flat band in which integer and fractional quantum Hall effect can be realized without an orbital magnetic field have been studied extensively. Realizing a topological flat band generally requires longer range hoppings in a lattice Hamiltonian. It is natural to ask what is the minimal hopping range required. In this letter, we prove that the mean hopping range of the flat-band Hamiltonian with Chern number C_1 and total number of bands N has a universal lower bound of √4│C_1│/πN Furthermore, for the Hamiltonians that reach this lower bound, the Bloch wavefunctions of the topological flat band are instanton solutions of a CP^(N-1)equation image non-linear σ model on the Brillouin zone torus, which are elliptic functions up to a normalization factor.

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Additional Information:© 2013 Wiley-VCH Verlag GmbH. Received 16 September 2012, revised 7 November 2012, accepted 8 November 2012. Published online 22 November 2012. CMJ and XLQ are supported by the David and Lucile Packard Foundation. ZCG is supported by Sherman Fairchild Foundation.
Group:Institute for Quantum Information and Matter
Funding AgencyGrant Number
David and Lucile Packard FoundationUNSPECIFIED
Sherman Fairchild FoundationUNSPECIFIED
Subject Keywords:Chern insulators, quantum Hall states, topological flat-band model, instanton solution, elliptic functions
Issue or Number:1-2
Record Number:CaltechAUTHORS:20130605-104157548
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Official Citation:Jian, C.-M., Gu, Z.-C. and Qi, X.-L. (2013), Momentum-space instantons and maximally localized flat-band topological Hamiltonians. Phys. Status Solidi RRL, 7: 154–156. doi: 10.1002/pssr.201206394
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:38810
Deposited By: Ruth Sustaita
Deposited On:05 Jun 2013 18:44
Last Modified:09 Nov 2021 23:40

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