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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$_{8+��}$ ($T_c$ = 66~K) despite the high carrier density. With a sign-problem free quantum Monte Carlo calculation, we show how a partially flat band at ($��$,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., main: 8 pages, 6 figures + supplement: 10 pages, 15 figures

Substrate engineering provides an opportunity to modulate the physical properties of quantum materials in thin film form. Here we report that TiSe$_2$ thin films grown on TiO$_2$ have unexpectedly large electron doping that suppresses the charge density wave (CDW) order. This is dramatically different from either bulk single crystal TiSe$_2$ or TiSe$_2$ thin films on graphene. The epitaxial TiSe$_2$ thin films can be prepared on TiO$_2$ via molecular beam epitaxy (MBE) in two ways: by conventional co-deposition using selenium and titanium sources, and by evaporating only selenium on reconstructed TiO$_2$ surfaces. Both growth methods yield atomically flat thin films with similar physical properties. The electron doping and subsequent suppression of CDW order can be explained by selenium vacancies in the TiSe$_2$ film, which naturally occur when TiO$_2$ substrates are used. This is due to the stronger interfacial bonding that changes the ideal growth conditions. Our finding provides a way to tune the chemical potential of chalcogenide thin films via substrate selection and engineering., 4 figures

We report a persistent low-energy phonon broadening around $q_{B} \sim 0.28$ r.l.u. along the Cu-O bond direction in the high-$T_c$ cuprate Bi$_2$Sr$_2$CaCu$_2$O$_{8+��}$ (Bi-2212). We show that such broadening exists both inside and outside the conventional charge density wave (CDW) phase, via temperature dependent measurements in both underdoped and heavily overdoped samples. Combining inelastic hard x-ray scattering, diffuse scattering, angle-resolved photoemission spectroscopy, and resonant soft x-ray scattering at the Cu $L_3$-edge, we exclude the presence of a CDW in the heavily overdoped Bi-2212 similar to that observed in the underdoped systems. Finally, we discuss the origin of such anisotropic low-energy phonon broadening, and its potential precursory role to the CDW phase in the underdoped region., 11 pages, 9 figures