Microwave spectroscopy of d-wave quasiparticles in highly underdoped YBCO

In the underdoped cuprates, photoemission and scanning-tunneling spectroscopies reveal that low energy quasiparticle excitations are confined to ``Fermi arcs" on the Brillouin zone diagonals. We have used microwave spectroscopy to probe these excitations with high resolution in high purity YBa$_2$Cu$_3$O$_{6+y}$. We have carried out detailed measurements of the superfluid density and conductivity as a function of doping, using a novel in-situ oxygen-ordering technique to tune doping in a single sample, in the range $T_c=20$~K to $T_c=0$~K. These measurements complement and extend the other spectroscopic measurements and show that nodal $d$-wave quasiparticles continue to exist as superconductivity is suppressed. We show that as the superconducting transition temperature $T_c$ is tuned to zero: the zero temperature superfluid density goes to zero; the maximum superconducting gap goes to zero; the gap slope softens; and Fermi liquid corrections cause the electrical current carried by the quasiparticles to decrease smoothly to zero.