Stability of nodal quasiparticles in underdoped YBa 2 Cu 3 O 6 + y probed by penetration depth and microwave spectroscopy

High-resolution measurements of superfluid density ${\ensuremath{\rho}}_{s}(T)$ and broadband quasiparticle conductivity ${\ensuremath{\sigma}}_{1}(\ensuremath{\Omega})$ have been used to probe the low-energy excitation spectrum of nodal quasiparticles in underdoped ${\text{YBa}}_{2}{\text{Cu}}_{3}{\text{O}}_{6+y}$. Penetration depth $\ensuremath{\lambda}(T)$ is measured to temperatures as low as 0.05 K. ${\ensuremath{\sigma}}_{1}(\ensuremath{\Omega})$ is measured from 0.1 to 20 GHz and is a direct probe of zero-energy quasiparticles. The data are compared with predictions for a number of theoretical scenarios that compete with or otherwise modify pure ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ superconductivity, in particular, commensurate and incommensurate spin and charge-density waves; ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+is$ and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$ superconductivity; circulating current phases; and the BCS-BEC crossover. We conclude that the data are consistent with a pure ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}$ state in the presence of a small amount of strong scattering disorder, and are able to rule out most candidate competing states either completely or to a level set by the energy scale of the disorder, ${T}_{d}\ensuremath{\sim}4\text{ }\text{K}$. Commensurate spin and charge-density orders, however, are not expected to alter the nodal spectrum and therefore cannot be excluded.