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Title: Optical spectral weight, phase stiffness, and T c bounds for trivial and topological flat band superconductors

We present exact results that give insight into how interactions lead to transport and superconductivity in a flat band where the electrons have no kinetic energy. We obtain bounds for the optical spectral weight for flat-band superconductors that lead to upper bounds for the superfluid stiffness and the two-dimensional (2D)Tc. We focus on on-site attraction|U|on the Lieb lattice with trivial flat bands and on the π-flux model with topological flat bands. For trivial flat bands, the low-energy optical spectral weightD̃lowñ|U|Ω/2withñ=minn,2n, where n is the flat-band density and Ω is the Marzari–Vanderbilt spread of the Wannier functions (WFs). We also obtain a lower bound involving the quantum metric. For topological flat bands, with an obstruction to localized WFs respecting all symmetries, we again obtain an upper bound forD̃lowlinear in|U|. We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results.

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Publication Date:
Journal Name:
Proceedings of the National Academy of Sciences
Page Range or eLocation-ID:
Article No. e2106744118
Proceedings of the National Academy of Sciences
Sponsoring Org:
National Science Foundation
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