Decrease of pairing strength with underdoping in cuprate superconductors

The transition temperature $T_{c}$ of cuprate superconductors decreases at low hole doping $p$, but it is still unclear whether the pairing strength decreases or increases. Different interpretations of the pseudogap lead to opposite conclusions. Different estimates of the upper critical field $H_{c2}$ are in sharp contradiction. In this talk, we resolve the latter contradiction by showing that superconducting fluctuations in the underdoped cuprate Eu-LSCO, measured via the Nernst effect, obey the theory of Gaussian fluctuations, as in conventional superconductors [1, 2]. The extracted critical field $H_{c2}$ is small, and it dips at $p$ = 0.11, showing that pairing strength is weak where stripe order is strong. In the archetypal cuprate superconductor YBCO, $H_{c2}$ extracted from other measurements~[3] has the same doping dependence, also with a minimum at $p$ = 0.11, again where stripe order is present [4, 5]. We conclude that competing states such as stripe order weaken the pairing strength and this, rather than phase fluctuations, is the predominant cause for the low $T_{c}$ of underdoped cuprates. Work done in collaboration with N. Doiron-Leyraud, E. Hassinger, J.-Ph. Reid, O. Cyr-Choini\`{e}re,~F. Lalibert\'{e}, R. Daou, S. Pyon, T. Takayama, H. Takagi,~~and Louis Taillefer. \\[4pt] [1] M. N. Serbyn \textit{et al}., Phys. Rev. Lett. \textbf{102}, 067001 (2009). \\[0pt] [2] K. Michaeli and A. M. Finkel'stein, Europhys. Lett. \textbf{86}, 27007 (2009).\\[0pt] [3] Y. Ando and K. Segawa, Phys. Rev. Lett. \textbf{88}, 167005 (2002).\\[0pt] [4] F. ~Lalibert\'{e}~\textit{et al.}, Nature Comm. \textbf{2}, 432 (2011).\\[0pt] [5] T. Wu \textit{et al}., Nature \textbf{477}, 191 (2011).