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Verma, Nishchhal ; Hazra, Tamaghna ; Randeria, Mohit ( , Proceedings of the National Academy of Sciences)
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)
. We focus on on-site attraction 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 weight with , 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 for linear in . We discuss the insights obtained from our bounds by comparing them with mean-field and quantum Monte Carlo results. -
Wu, Guanzhong ; Wang, Dongying ; Verma, Nishchhal ; Rao, Rahul ; Cheng, Yang ; Guo, Side ; Cao, Guixin ; Watanabe, Kenji ; Taniguchi, Takashi ; Lau, Chun Ning ; et al ( , Nano Letters)