Welcome to the new version of CaltechAUTHORS. Login is currently restricted to library staff. If you notice any issues, please email coda@library.caltech.edu
Published February 2013 | public
Journal Article

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

Abstract

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.

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.

Additional details

Created:
August 19, 2023
Modified:
October 23, 2023