Interactions between nematic fluctuations, magnetic order and superconductivity are central to the physics of iron-based superconductors. Here we report on in-plane transverse acoustic phonons in hole-doped Sr1−xNaxFe2As2 measured via inelastic x-ray scattering, and extract both the nematic susceptibility and the nematic correlation length. By a self-contained method of analysis, for the underdoped (x=0.36) sample, which harbors a magnetically ordered tetragonal phase, we find it hosts a short nematic correlation length ξ∼10  Å and a large nematic susceptibility χnem. The optimal-doped (x=0.55) sample exhibits weaker phonon softening effects, indicative of both reduced ξ and χnem. Our results suggest short-range nematic fluctuations may favor superconductivity, placing emphasis on the nematic correlation length for understanding the iron-based superconductors.

Fluctuating superconductivity—vestigial Cooper pairing in the resistive state of a material—is usually associated with low dimensionality, strong disorder, or low carrier density. Here, we report single-particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in the heavily hole-doped cuprate superconductor () despite the high carrier density. With a sign-problem-free quantum Monte Carlo calculation, we show how a partially flat band at can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.

Fluctuating superconductivity - vestigial Cooper pairing in the resistive state of a material - is usually associated with low dimensionality, strong disorder or low carrier density. Here, we report single particle spectroscopic, thermodynamic and magnetic evidence for persistent superconducting fluctuations in heavily hole-doped cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($\pi$,0) can help enhance superconducting phase fluctuations. Finally, we discuss the implications of an anisotropic band structure on the phase-coherence-limited superconductivity in overdoped cuprates and other superconductors.