Doping evolution of nodal quasiparticle velocities in cuprate superconductors

The thermal conductivity of the cuprate superconductor YBa$_2$Cu$_3$O$_y$ was measured at temperatures down to $T \sim 50$~mK on high-quality single crystals with a hole doping ranging from $p = 0.06$ to $p = 0.18$. The residual linear term at $T \to 0$ is a direct measure of the ratio of nodal quasiparticle velocities. When combined with published data on Tl$_2$Ba$_2$CuO$_{6+\delta}$ [1], our data spans the full superconducting phase. The ratio of quasiparticle velocities agrees well with recent, high-resolution ARPES measurements of the Fermi velocity and gap velocity at the nodes as a function of doping, in the related cuprate superconductor Bi$_2$Sr$_2$CaCu$_2$O$_{8+\delta}$ [2,3]. \\[4pt] [1] D.G. Hawthorn {\it et al.}, Phys. Rev. B {\bf 75}, 104518 (2007). \\[0pt] [2] I.M. Vishik {\it et al.}, Phys. Rev. Lett. {\bf 104}, 207002 (2010). \\[0pt] [3] I.M. Vishik {\it et al.}, ArXiv, 1209.6514 (2012).