Ultrasonic signatures at the superconducting and the pseudogap phase boundaries in YBCO cuprates

A major issue in the understanding of cuprate superconductors is the nature of the metallic state from which high temperature superconductivity emerges. Central to this issue is the pseudogap region of the doping-temperature phase diagram that extends from room temperature to the superconducting transition. Although polarized neutron scattering studies hint at magnetic order associated with the pseudogap, there is no clear thermodynamic evidence for a phase boundary. Such evidence has a straightforward physical interpretation, however, it is difficult to obtain over a temperature range wide enough to encompass both the pseudogap and superconducting phases. We address this by measuring the elastic response of detwinned single crystals, an underdoped YBCO{sub 6.60} with superconducting transition at T{sub c} = 61.6K and a slightly overdoped YBCO{sub 6.98} with T{sub c} = 88.0K. We observe a discontinuity in the elastic moduli across the superconducting transition. Its magnitude requires that pair formation is coincident with superconducting coherence (the onset of the Meissner effect). For both crystals the elastic response reveals a phase transition at the pseudogap boundary. In slightly overdoped YBCO that transition is 20K below T{sub c}, extending the pseudogap phase boundary inside the superconducting dome. This supports a description of the metallic state in cuprates where a pseudogap phase boundary evolves into a quantum critical point masked by the superconducting dome.