Doping dependence of the upper critical field $H_{\rm c2}$ in the cuprate superconductor YBCO

It is generally thought that the upper critical field $H_{\rm c2}$ of underdoped cuprate superconductors is far greater than the vortex-solid melting field $H_{\rm vs}$ at which the state of zero resistance ends, even at $T = 0$ [1]. Here we compare electrical measurements of $H_{\rm vs}$ and thermal measurements of $H_{\rm c2}$ [2] in the cuprate YBCO and show that $H_{\rm c2} = H_{\rm vs}$ at $T \to 0$, strong evidence that there is no vortex liquid phase at $T = 0$. We then present extensive measurements of the electrical resistivity in high magnetic fields over a wide doping range, from which we obtain $H_{\rm c2}$ as a function of doping in YBCO. We find that $H_{\rm c2}$ collapses to remarkably low values in the underdoped regime, which we attribute to the competing effect of a phase with charge-density-wave order [3, 4], also responsible for a reconstruction of the Fermi surface [5, 6].\\[4pt] [1] T. Senthil and P.A. Lee, Phys. Rev. B {\bf 79}, 245116 (2009).\\[0pt] [2] See~APS~talk~by~G.~Grissonnanche.\\[0pt] [3] T. Wu \textit{et~al.}, Nature {\bf 477}, 191 (2011).\\[0pt] [4] G. Ghiringhelli \textit{et~al.}, Science {\bf 337}, 821 (2012).\\[0pt] [5] D. LeBoeuf \textit{et~al.}, Phys. Rev. B {\bf 83}, 054506 (2011).\\[0pt] [6] N. Doiron-Leyraud and L. Taillefer, Physica C {\bf 481}, 161 (2012).