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I will show that optical spectral weight puts an upper bound on the superfluid stiffness of multi-band systems with arbitrary interactions in any dimension. This in turn leads to a bound [1] on the BKT Tc in 2D, independent of pairing mechanism, that is particularly useful for strongly correlated materials. The result simplifies to Tc/Tf < 1/8 for a parabolic band, an exact result across the BCS-BEC crossover, that has been tested in recent experiments [2]. I will then describe results for multi-band systems with complex band structures like twisted bilayer graphene. Next, I will turn to flat band superconductivity [3] and describe bounds on the low-energy optical spectral weight in terms of the “quantum geometry” of the Wannier functions in both trivial and topological flat bands. Finally, I will discuss the open problem of deriving Tc bounds in 3D.
[1] T. Hazra, N. Verma, M. Randeria, Phys. Rev. X 9, 031049 (2019)
[2] Y. Nakagawa et al., Science 372, 190 (2021)
[3] N. Verma, T. Hazra, M. Randeria, Proc. Nat. Acad. Sci. 118, e2106744118 (2021) |