We present a theoretical framework for understanding the behavior of the normal and superconducting states of overdoped cuprate high temperature superconductors in the vicinity of the doping-tuned quantum superconductor-to-metal transition. The key ingredients on which we focus are d-wave pairing, a flat antinodal dispersion, and disorder. Even for homogeneous disorder, these lead to effectively granular superconducting correlations and a superconducting transition temperature determined in large part by the superfluid stiffness rather than the pairing scale.

We study strong electron-phonon interacting systems where the geometry of the crystalline lattice frustrates the formation of charge order. Our results show that under such condition, high-Tc superconductivity can occur in a wide range of electron-phonon coupling strengths. This result is obtained by studying the Holstein model on triangular lattice using sign-problem-free quantum Monte Carlo method.

Monolayer FeSe films grown on SrTiO₃ (STO) substrate show superconducting gap-opening temperatures ([Formula: see text]) which are almost an order of magnitude higher than those of the bulk FeSe and are highest among all known Fe-based superconductors. Angle-resolved photoemission spectroscopy observed "replica bands" suggesting the importance of the interaction between FeSe electrons and STO phonons. These facts rejuvenated the quest for [Formula: see text] enhancement mechanisms in iron-based, especially iron-chalcogenide, superconductors. Here, we perform the first numerically-exact sign-problem-free quantum Monte Carlo simulations to iron-based superconductors. We (1) study the electronic pairing mechanism intrinsic to heavily electron doped FeSe films, and (2) examine the effects of electron-phonon interaction between FeSe and STO as well as nematic fluctuations on [Formula: see text]. Armed with these results, we return to the question "what makes the [Formula: see text] of monolayer FeSe on SrTiO₃ so high?" in the conclusion and discussions.

The microscopic mechanism for the disappearance of superconductivity in overdoped cuprates is still under heated debate. Here we use scanning tunneling spectroscopy to investigate the evolution of quasiparticle interference phenomenon in Bi₂Sr₂CuO_6+δ over a wide range of hole densities. We find that when the system enters the overdoped regime, a peculiar quasiparticle interference wavevector with arc-like pattern starts to emerge even at zero bias, and its intensity grows with increasing doping level. Its energy dispersion is incompatible with the octet model for d-wave superconductivity, but is highly consistent with the scattering interference of gapless normal carriers. The gapless quasiparticles are mainly located near the antinodes and are independent of temperature, consistent with the disorder scattering mechanism. We propose that a branch of normal fluid emerges from the pair-breaking scattering between flat antinodal bands in the quantum ground state, which is the primary cause for the reduction of superfluid density and suppression of superconductivity in overdoped cuprates.

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.