Understanding the normal state and the mechanism controlling the superconducting (SC) transition temperature T_c⁰ as a function of doping are central questions in cuprate high-temperature superconductors. While in underdoped cuprates T_c⁰ is set by global phase coherence rather than the scale of pairing, the role of SC phase fluctuations and the origin of the strange metal behavior in the overdoped region remain controversial. This talk will describe transport measurements in perpendicular magnetic fields (H) on Bi_2+xSr_2-x-yLa_yCuO_6+d (Bi-2201) cuprates for doping levels from underdoped to heavily overdoped. In contrast to the La-214 family, Bi-2201 exhibits only short-range charge order, with no evidence of spin order. In the underdoped region, immeasurably small Hall response for T>T_c(H) is revealed as a signature of a SC regime with vortexlike phase fluctuations. The extent of this regime in T and H is suppressed near optimal doping but strongly enhanced in heavily overdoped Bi-2201. These results demonstrate that vortexlike phase fluctuations play a key role in the field-tuned SC transition in the heavily overdoped region, in contrast to conventional mean-field Bardeen-Cooper-Schrieffer description. Their unexpected nonmonotonic doping dependence provides a new perspective on the superconducting transition in cuprates. The relationship to the strange metal regime, the roles of disorder, charge order, and of the intrinsically two-dimensional nature of cuprates will be also discussed.

Terzic, J., Pokharel, B.K., Li, Z. et al. Persistence of vortexlike phase fluctuations in underdoped to heavily overdoped cuprates. Nat Commun 17, 805 (2026). https://doi.org/10.1038/s41467-025-67503-z